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Measure functional differential equations and functional dynamic equations on time scales

Federson, Márcia Cristina Anderson Braz; Mesquita, Jaqueline Godoy; Slavik, Antonin
Fonte: ACADEMIC PRESS INC ELSEVIER SCIENCE; SAN DIEGO Publicador: ACADEMIC PRESS INC ELSEVIER SCIENCE; SAN DIEGO
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
86.18%
We study measure functional differential equations and clarify their relation to generalized ordinary differential equations. We show that functional dynamic equations on time scales represent a special case of measure functional differential equations. For both types of equations, we obtain results on the existence and uniqueness of solutions, continuous dependence, and periodic averaging.; FAPESP [2010/09139-3, 2010/12673-1]; CNPq [304646/2008-3]; CAPES [6829-10-4]; Czech Ministry of Education [MSM 0021620839]

Boundedness of solutions of retarded functional differential equations with variable impulses via generalized ordinary differential equations

Afonso, Suzete Maria Silva; Bonotto, Everaldo de Mello; Federson, Márcia Cristina Anderson Braz; Gimenes, L. P.
Fonte: WILEY-V C H VERLAG GMBH; WEINHEIM Publicador: WILEY-V C H VERLAG GMBH; WEINHEIM
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
96.21%
In this paper, we give sufficient conditions for the uniform boundedness and uniform ultimate boundedness of solutions of a class of retarded functional differential equations with impulse effects acting on variable times. We employ the theory of generalized ordinary differential equations to obtain our results. As an example, we investigate the boundedness of the solution of a circulating fuel nuclear reactor model.

Periodic averaging theorems for various types of equations

Mesquita, Jaqueline Godoy; Slavik, Antonin
Fonte: ACADEMIC PRESS INC ELSEVIER SCIENCE; SAN DIEGO Publicador: ACADEMIC PRESS INC ELSEVIER SCIENCE; SAN DIEGO
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
76.28%
We prove a periodic averaging theorem for generalized ordinary differential equations and show that averaging theorems for ordinary differential equations with impulses and for dynamic equations on time scales follow easily from this general theorem. We also present a periodic averaging theorem for a large class of retarded equations.; FAPESP [2010/12673-1]; CAPES [6829-10-4]; Czech Ministry of Education [MSM 0021620839]

Método da média para equações diferenciais funcionais retardadas impulsivas via equações diferenciais generalizadas; Averaging method for retarded functional differential equations with impulses by generalized ordinary differential equations

Godoy, Jaqueline Bezerra
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 24/08/2009 PT
Relevância na Pesquisa
76.15%
Neste trabalho, nós consideramos o seguinte problema de valor inicial para uma equação diferencial funcional retardada com impulsos { 'x PONTO' = 'varepsilon' f (t, 'x IND.t'), t ' DIFERENTE' 't IND. k', 'DELTA' x('t IND. k') = 'varepsilon' ' I IND. k' (x ( 't IND.k')), k = 0, 1, 2, ... 'x IND. t IND.0' = ' phi', onde f está definida em um aberto ' OMEGA' de R x ' G POT. -' ([- r, 0], ' R POT. n') e assume valores em 'R POT. n', ' 'varepsilon' 'G POT. - ([ - r, 0], 'R POT.n'), r .0, onde ' G POT -' ([ - r, 0], ' R POT. n') denota o espaço das funções de [ - r, 0] em ' R POT. n' que estão regradas e contínuas à esquerda. Além disso, ' t IND.0 < ' t IND. 1'< ... 't IND. k' < ... são momentos pré determinados de impulsos tais que 'lim SOBRE k SETA + ' INFINITO' 't IND. k = + ' INFINITO' e 'DELTA'x (' t IND.k') = x ( 't POT. + IND > k) - x ('t IND. k). Os operadores de impulso ' I IND. k', k = 0, 1, ... são funções contínuas de 'R POT. n' em ' R POT. n'. Consideramos, também, que para cada x 'varepsilon' ' G POT. -' ([- r, ' INFINITO'), 'R POT. n'), t 'SETA' f (t, 'x IND. t') é uma função localmente Lebesgue integrável e sua integral indefinida satisfaz uma condição do tipo Carathéodory. Além disso, f é Lipschitziana na segunda variável. Definimos ' f IND. 0' ( 'phi') = ' lim SOBRE T ' SETA' ' INFINITO' '1 SUP. T ' INT. SUP. T INF. ' T IND.0' f (t...

Equações diferenciais funcionais com retardamento e impulsos em tempo variável via equações diferenciais ordinárias generalizadas; Retarded functional differential equations with variable impulses via generalized ordinary differential equations

Afonso, Suzete Maria Silva
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 15/02/2011 PT
Relevância na Pesquisa
96.21%
O objetivo deste trabalho é investigar propriedades qualitativas das soluções de equações diferenciais funcionais com retardamento e impulsos em tempo variável (EDFRs impulsivas) através da teoria de equações diferenciais ordinárias generalizadas (EDOs generalizadas). Nossos principais resultados dizem respeito a estabilidade uniforme, estabilidade uniforme assintótica e estabilidade exponencial da solução trivial de uma determinada classe de EDFRs com impulsos em tempo variável e limitação uniforme de soluções da mesma classe. A fim de obtermos tais resultados para EDFRs com impulsos em tempo variável, estabelecemos novos resultados sobre propriedades qualitativas das soluções de EDOs generalizadas. Assim, portanto, este trabalho contribui para o desenvolvimento de ambas as teorias de EDFRs com impulsos e de EDOs generalizadas. Os resultados novos apresentados neste trabalho estão contidos nos artigos [1], [2] e [3]; The purpose of this work is to investigate qualitative properties of solutions of retarded functional differential equations (RFDEs) with impulse effects acting on variable times using the theory of generalized ordinary differential equations (generalized ODEs). Our main results concern uniform stability...

Equações diferenciais ordinárias generalizadas e aplicações às equações diferenciais clássicas; Generalized ordinary differential equations and applications to classical differential equations

Toon, Eduard
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 21/08/2012 PT
Relevância na Pesquisa
86.34%
O objetivo deste trabalho e estudar algumas propriedades de soluções de equações diferenciais ordinárias generalizadas e aplicar tais resultados a algumas equações diferenciais clássicas (equações diferenciais ordinárias abstratas e equações diferenciais funcionais em medida). Os principais resultados tratam de existência-unicidade de soluções para uma classe de equações diferenciais ordinárias generalizadas, dependência contnua de soluções com respeito as condições iniciais e bacia de atração. Estes resultados são transferidos para uma classe de equações diferencias ordinárias abstratas. Também obtemos resultados sobre estabilidade da solução trivial de equações diferenciais ordinárias generalizadas e transferimos estes resultados para uma classe de equações diferenciais funcionais em medida; The purpose of this work is to study some properties of solutions of generalized ordinary dierential equations and apply these results to some classical dierential equations (abstract ordinary dierential equations and measure functional dierential equations). The main results concern existence-uniqueness of a solution for a class of generalized ordinary dierential equations, continuous dependence of solutions with respect to initial conditions and basin of attraction. These results are transfered to a class of abstract ordinary dierential equations. We also obtain some results on the stability of the trivial solution of generalized ordinary dierential equations and we transfer these results to a class of measure functional dierential equations

Equações diferenciais ordinárias generalizadas lineares e aplicações às equações diferenciais funcionais lineares; Linear generalized ordinary differential equations and application to linear functional differential equations

Collegari, Rodolfo
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 25/02/2014 PT
Relevância na Pesquisa
96.3%
Neste trabalho, apresentamos uma fórmula da variação das constantes para EDOs generalizadas lineares em espaços de Banach. Mais especificamente, estamos interessados em estabelecer uma relação entre as soluções do problema de Cauchy para uma EDO generalizada linear 'dx SUP. d 'tau' =D[A(t )x], x('t IND. 0') = 'x SOB. ~' e as soluções do problema de Cauchy perturbado 'dx SUP. d 'tau' =D[A(t )x +F(x, t )], x('t IND. 0') = x('t IND. 0') = 'x SOB. ~' , em que as funções envolvidas são Perron integráveis e, portanto, admitem muitas descontinuidades e oscilações. Também provamos a existência de uma correspondência biunívoca entre o problema de Cauchy para uma EDF linear da forma { ' y PONTO' =L(t )'y IND. t' , 'y IND. t IND. 0 = \varphi', , em que L é um operador linear e limitado e 'varphi' é uma função regrada, e uma certa classe de EDOs generalizadas lineares. Como consequência, obtemos uma fórmula da variação das constantes relacionando as soluções da EDF linear e as soluções do problema perturbado { 'y PONTO' = L(t )'y IND.t' + f ('yIND. t' , 'y IND. t IND. 0' = '\varphi ', em que a aplicação 't SETA ' f ('y IND. t' , t) é Perron integrável, com t em um intervalo de R, para cada função regrada y; In this work...

Rational General Solutions of Systems of Autonomous Ordinary Differential Equations of Algebro-Geometric Dimension One

Lastra Sedano, Alberto; Sendra Pons, Juan Rafael; Ngo, L. X. Chau; Winkler, Franz
Fonte: Debrecen Publ. Math. Debrecen Publicador: Debrecen Publ. Math. Debrecen
Tipo: info:eu-repo/semantics/article; info:eu-repo/semantics/acceptedVersion Formato: application/pdf
ENG
Relevância na Pesquisa
96.23%
The final journal version of this paper appears in A. Lastra, J. R. Sendra, L. X. C. Ngô and F. Winkler (2014). Rational General Solutions of Systems of Autonomous Ordinary Differential Equations of Algebro- Geometric Dimension One. Publ. Math. Debrecen Publ. Math. Debrecen 2015 / 86 / 1-2 49–69. DOI: 10.5486/PMD.2015.6032 and it is available at http://dx.doi.org/10.5486/PMD.2015.6032; An algebro-geometric method for determining the rational solvability of autonomous algebraic ordinary differential equations is extended from single equations of order 1 to systems of equations of arbitrary order but dimension 1 in the algebrogeometric sense. We provide necessary conditions, for the existence of rational solutions, on the degree and on the structure at infinity of the associated algebraic curve. Furthermore, from a rational parametrization of a planar projection of the corresponding space curve one deduces, either by derivation or by lifting the planar parametrization, the existence and actual computation of all rational solutions if they exist. Moreover, if the differential polynomials are defined over the rational numbers, we can express the rational solutions over the same field of coefficients.; Vietnam Institute for Advanced Study in Mathematics (VIASM)

On second-order differential equations with highly oscillatory forcing terms

Condon, Marissa; Deaño, Alfredo; Iserles, Arieh
Fonte: The Royal Society Publicador: The Royal Society
Tipo: info:eu-repo/semantics/acceptedVersion; info:eu-repo/semantics/article Formato: application/pdf; text/plain
Publicado em //2010 ENG
Relevância na Pesquisa
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We present a method to compute efficiently solutions of systems of ordinary differential equations (ODEs) that possess highly oscillatory forcing terms. This approach is based on asymptotic expansions in inverse powers of the oscillatory parameter, and features two fundamental advantages with respect to standard numerical ODE solvers: first, the construction of the numerical solution is more efficient when the system is highly oscillatory, and, second, the cost of the computation is essentially independent of the oscillatory parameter. Numerical examples are provided, featuring the Van der Pol and Duffing oscillators and motivated by problems in electronic engineering.; A. Deaño acknowledges financial support from the Spanish Ministry of Education under the programme of postdoctoral grants (Programa de becas postdoctorales) and project MTM2006-09050. The material is based upon works supported by Science Foundation Ireland under Principal Investigator Grant No. 05/IN.1/I18.

Software for the parallel solution of systems of ordinary differential equations

Lustman, Levi; Neta, Beny
Fonte: Monterey, California. Naval Postgraduate School Publicador: Monterey, California. Naval Postgraduate School
Tipo: Relatório Formato: 28 p. ; 28 cm.
EN_US
Relevância na Pesquisa
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Approved for public release; distribution unlimited.; In this report we supply software for the numerical solution of systems of ordinary differential equations (ODEs) on an INTEL iPSC/2 hypercube. The first program can only be used to solve linear initial or boundary value systems of ODEs and based on an algorithm developed by Katti and Neta (1989) and improved by Lustman et al (1990). The second program is based on polynomial extrapolation and Gragg's scheme and is useful for nonlinear ODEs as well. This algorithm is described in Lustman, Neta and Gragg (1991); http://archive.org/details/softwareforparal00lust

Demonstrações assistidas por computador para equações diferenciais ordinárias; Computer assisted proof for ordinary differential equations

Prado, Mário César Monteiro do
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 23/02/2015 PT
Relevância na Pesquisa
86.04%
Neste trabalho, apresentamos um método computacional rigoroso para a demonstração de existência de órbitas periódicas de alguns sistemas de equações diferenciais ordinárias com campo autônomo do tipo polinomial. Mostraremos que o problema de encontrar órbitas periódicas para esses sistemas de equações é equivalente a buscar por raízes de certas funções definidas no espaço de Banach das sequências com decaimento algébrico. O método pode ser dividido em duas etapas. Na primeira, buscamos numericamente por soluções periódicas aproximadas. Na segunda, mostraremos a existência de uma órbita periódica numa vizinhança da curva encontrada numericamente. O rigor das verificações computacionais é garantido pelo uso de aritimética intervalar.; In this work, we present a rigorous computational method for proving the existence of periodic orbits of some systems of ordinary differential equations with autonomous vector field of polynomial type. We show that the problem of finding periodic orbits for these systems is equivalent to check for roots of certain functions defined in the Banach space of sequences with algebraic decay. The method can be divided into two steps. First, we seek, numerically, to approximated periodic solutions. Then...

Equações diferenciais ordinarias com campo de direções parcialmente conhecido; Ordinary differential equations with direction field partly known

Marina Ribeiro Barros Dias
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 26/04/2006 PT
Relevância na Pesquisa
96.15%
Nesse trabalho propomos uma metodologia para o estudo de Equações Diferenciais Ordinárias cujo campo de direções é apenas parcialmente conhecido. Para isto, aliamos a teoria de controladores fuzzy com métodos numéricos tradicionais. A partir de teoremas clássicos de continuidade e estudos sobre aproximação, vimos que, para alguns casos, as soluções aqui produzidas aproximam-se das teóricas. Fazemos uso da metodologia aqui proposta para analisar modelos de crescimento populacional de espécie isolada e também modelos que envolvem várias espécies. Finalmente, indicamos essa metodologia como uma ferramenta auxiliar para obtenção de parâmetros de equações diferenciais determinísticas; In this work we propose a metodology to study Ordinary Differential Equations supposing the direction field is partially known. We join theory of Fuzzy Controlers and traditional numerical methods to develop this study. Using classical theorems of continuity and aproximation theory we saw that, for some cases, the solutions we present here estimate the theorical ones. We'll use the metodology proposed here to analyse unidimensional models of populational growth and models that envolves many species. Finally, we point out our metodology like an auxiliar tool to obtain parameters of deterministic differential equations

18.03 Differential Equations, Spring 2004; Differential Equations

Miller, Haynes R., 1948-; Mattuck, Arthur
Fonte: MIT - Massachusetts Institute of Technology Publicador: MIT - Massachusetts Institute of Technology
Formato: 15763 bytes; 21400 bytes; 19396 bytes; 52967 bytes; 26276 bytes; 20464 bytes; 24257 bytes; 25098 bytes; 16631 bytes; 16938 bytes; 17311 bytes; 34298 bytes; 17352 bytes; 14476 bytes; 4586 bytes; 18637 bytes; 11602 bytes; 18220 bytes; 4755 bytes; 27322 byte
EN-US
Relevância na Pesquisa
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Study of ordinary differential equations, including modeling of physical problems and interpretation of their solutions. Standard solution methods for single first-order equations, including graphical and numerical methods. Higher-order forced linear equations with constant coefficients. Complex numbers and exponentials. Matrix methods for first-order linear systems with constant coefficients. Non-linear autonomous systems; phase plane analysis. Fourier series; Laplace transforms.

Geometric Linearization of Ordinary Differential Equations

Qadir, Asghar
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
76.14%
The linearizability of differential equations was first considered by Lie for scalar second order semi-linear ordinary differential equations. Since then there has been considerable work done on the algebraic classification of linearizable equations and even on systems of equations. However, little has been done in the way of providing explicit criteria to determine their linearizability. Using the connection between isometries and symmetries of the system of geodesic equations criteria were established for second order quadratically and cubically semi-linear equations and for systems of equations. The connection was proved for maximally symmetric spaces and a conjecture was put forward for other cases. Here the criteria are briefly reviewed and the conjecture is proved.; Comment: This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

A geometric setting for systems of ordinary differential equations

Bucataru, Ioan; Constantinescu, Oana; Dahl, Matias F.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 26/11/2010
Relevância na Pesquisa
76.2%
To a system of second order ordinary differential equations (SODE) one can assign a canonical nonlinear connection that describes the geometry of the system. In this work we develop a geometric setting that allows us to assign a canonical nonlinear connection also to a system of higher order ordinary differential equations (HODE). For this nonlinear connection we develop its geometry, and explicitly compute all curvature components of the corresponding Jacobi endomorphism. Using these curvature components we derive a Jacobi equation that describes the behavior of nearby geodesics to a HODE. We motivate the applicability of this nonlinear connection using examples from the equivalence problem, the inverse problem of the calculus of variations, and biharmonicity. For example, using components of the Jacobi endomorphism we express two Wuenschmann-type invariants that appear in the study of scalar third or fourth order ordinary differential equations.

Numerical methods for systems of highly oscillatory ordinary differential equations

Khanamiryan, Marianna
Fonte: University of Cambridge; Department of Applied Mathematics and Theoretical Physics Publicador: University of Cambridge; Department of Applied Mathematics and Theoretical Physics
Tipo: Thesis; doctoral; PhD
EN
Relevância na Pesquisa
96.26%
Current research made contribution to the numerical analysis of highly oscillatory ordinary differential equations. Highly oscillatory functions appear to be at the forefront of the research in numerical analysis. In this work we developed efficient numerical algorithms for solving highly oscillatory differential equations. The main important achievements are: to the contrary of classical methods, our numerical methods share the feature that asymptotically the approximation to the exact solution improves as the frequency of oscillation grows; also our methods are computationally feasible and as such do not require fine partition of the integration interval. In this work we show that our methods introduce better accuracy of approximation as compared with the state of the art solvers in Matlab and Maple.; This thesis presents methods for efficient numerical approximation of linear and non-linear systems of highly oscillatory ordinary differential equations. Phenomena of high oscillation is considered a major computational problem occurring in Fourier analysis, computational harmonic analysis, quantum mechanics, electrodynamics and fluid dynamics. Classical methods based on Gaussian quadrature fail to approximate oscillatory integrals. In this work we introduce numerical methods which share the remarkable feature that the accuracy of approximation improves as the frequency of oscillation increases. Asymptotically...

Quantised State Simulation (QSS): Advances in the Numerical Solution of Ordinary Differential Equations

Vassiliadis, Vassilios S.; Fiorelli, Fabio
Fonte: Universidade de Cambridge Publicador: Universidade de Cambridge
Tipo: Conferência ou Objeto de Conferência
EN
Relevância na Pesquisa
86.2%
This presentation handout presents the idea of discretising the state variables (quantising them) instead of time, to effect the numerical integration/simulation of ordinary differential equation systems. The aim is to provide the computational technology to address huge scale systems at extremely high efficiency, at unprecedented speeds over existing methods. The methodology results in a matrix free algorithm, which can also be very readily be used for sensitivity evaluations and is highly parallelisable (in fact it is completely scalable). A multitude of potential uses is outlined, i.e. replacing totally the need for stochastic simulation algorithms for dynamical systems as the method is completely rigorous and robust, and nonrandom. In other words it comprises an innovative standard type numerical integration scheme. The potential for applications in Molecular Dynamic Simulation, Polymerisation reaction simulations, population dynamic balances, and of course in combustion reactions is tremendous. The importance also and its particular incomparable strength over stochastic simulation methods is that it can produce rigorous high precision values for sensitivity equations. As such it can be integrated within a parameter estimation scheme robustly...

Parameter estimation of ordinary differential equations

Li, Zheng Feng; Osborne, Michael; Prvan, Tania
Fonte: Oxford University Press Publicador: Oxford University Press
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
96.1%
This paper addresses the development of a new algorithm for parameter estimation of ordinary differential equations. Here, we show that (1) the simultaneous approach combined with orthogonal cyclic reduction can be used to reduce the estimation problem to an optimization problem subject to a fixed number of equality constraints without the need for structural information to devise a stable embedding in the case of non-trivial dichotomy and (2) the Newton approximation of the Hessian information of the Lagrangian function of the estimation problem should be used in cases where hypothesized models are incorrect or only a limited amount of sample data is available. A new algorithm is proposed which includes the use of the sequential quadratic programming (SQP) Gauss-Newton approximation but also encompasses the SQP Newton approximation along with tests of when to use this approximation. This composite approach relaxes the restrictions on the SQP Gauss-Newton approximation that the hypothesized model should be correct and the sample data set large enough. This new algorithm has been tested on two standard problems.

Symmetries and integration of differential equations

Torres del Castillo,Gerardo; Marciano Melchor,Magdalena
Fonte: Revista Colombiana de Matemáticas Publicador: Revista Colombiana de Matemáticas
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/12/2005 EN
Relevância na Pesquisa
86.1%
A proof of the Lie theorem which relates the symmetries of a first order differential equation (or of a linear differential form) with its integrating factors is given. It is shown that a similar result partially applies for systems of linear differential forms and ordinary differential equations of any order.

Modified nonlinearities distribution Homotopy Perturbation method as a tool to find power series solutions to ordinary differential equations

Filobello-Nino,U.; Vázquez-Leal,H.; Khan,Y.; Pereyra-Díaz,D.; Pérez-Sesma,A.; Díaz-Sánchez,A.; Jiménez-Fernández,V.M.; Herrera-May,A.; López-Martínez,R.; Sanchez-Orea,J.
Fonte: Universidad de La Salle Bajío A. C., Coordinación de Investigación Publicador: Universidad de La Salle Bajío A. C., Coordinación de Investigación
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/01/2014 EN
Relevância na Pesquisa
86.07%
In this article, modified non-linearities distribution homotopy perturbation method (MNDHPM) is used in order to find power series solutions to ordinary differential equations with initial conditions, both linear and nonlinear. We will see that the method is particularly relevant in some cases of equations with non-polynomial coefficients and inhomogeneous non-polynomial terms.