NUMERICAL FINDING OF SOLUTIONS TO HYPERBOLIC DIFFERENTIAL EQUATIONS BY THE GRID METHOD
Keywords:
differential equations, grid method, difference schemes, approximation, numerical methods, partial derivatives, finite difference method, computational experimentAbstract
This article is devoted to the numerical solution of differential equations. A method for solving a hyperbolic differential equation defined in a limited interval [0,1] based on given conditions is demonstrated using the grid method, which is one of the numerical methods. Particular attention is paid to the application of the grid method to approximating first- and second-order partial derivatives. The basic principles of constructing uniform and non-uniform grids are presented, and left, right, and central difference schemes, as well as their approximation order, are considered. A computational scheme for the numerical solution of the Cauchy problem is developed based on difference substitutions. The obtained numerical results are compared with analytical values, confirming the efficiency and accuracy of the proposed method
