Numerical Solutions of Hyperbolic Partial Differential Equations

Abstract

Hyperbolic partial differential equations are frequently referenced in modeling real-world problems in mathematics and engineering. In this study, a matrix method based on collocation points and Taylor polynomials is presented to obtain the approximate solution of the hyperbolic partial differential equation. This technique reduces the solution of the mentioned hyperbolic partial differential equation under initial and boundary conditions to the solution of a matrix equation whose Taylor coefficients are unknown. Thus, the approximate solution is obtained in terms of Taylor polynomials. An example is provided to showcase the practical application of the technique. In addition, the numerical results obtained using these collocation points were compared with the table and figure. All numerical calculations were made on the computer using a program written in WOLFRAM MATHEMATICA 13.0.