Numerical Solutions of Hyperbolic Partial Differential Equations

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