A feasible numerical computation based on matrix operations and collocation points to solve linear system of partial differential equations

In this work, a system of linear partial differential equations with constant and variable coefficients via Cauchy conditions is handled by applying the numerical algorithm based on operational matrices and equally-spaced collocation points. To demonstrate the applicability and efficiency of the met...

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Vydáno v:Journal of computational science Ročník 83; s. 102445
Hlavní autoři: Çayan, Seda, Sezer, Mehmet
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.12.2024
Témata:
Collocation points
Initial value problem
Operational matrices
System of partial differential equations
Truncated series
Collocation points
System of partial differential equations
Operational matrices
Truncated series
Initial value problem
ISSN:1877-7503
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Shrnutí:In this work, a system of linear partial differential equations with constant and variable coefficients via Cauchy conditions is handled by applying the numerical algorithm based on operational matrices and equally-spaced collocation points. To demonstrate the applicability and efficiency of the method, four illustrative examples are tested along with absolute error, maximum absolute error, RMS error, and CPU times. The approximate solutions are compared with the analytical solutions and other numerical results in literature. The obtained numerical results are scrutinized by means of tables and graphics. These comparisons show accuracy and productivity of our method for the linear systems of partial differential equations. Besides, an algorithm is described that summarizes the formulation of the presented method. This algorithm can be adapted to well-known computer programs. •We developed a novel numerical algorithm for the solution of a linear system of PDEs subject to initial conditions.•The classical matrix collocation method is modified and extended to solve the system of PDEs for the first time.•Comparisons with the analytical and numerical solutions reveal that the presented method is highly effective and convenient.•The main advantages of our method are its straightforward application and produce reliable results.
ISSN:1877-7503
DOI:10.1016/j.jocs.2024.102445