Right-hand side method for the numerical solution of nonlinear partial differential equations

The paper proposes a right-hand side method for the numerical solution of nonlinear partial differential equations. The class of differential equations with partial time derivatives on the left-hand side is considered. The solutions of these equations are represented by continuous functions of time and spatial coordinates. By integrating over time, the original differential equations are written in an implicit difference form. The algorithm of the method is given. An example of solving a one-dimensional hyperbolic equation by this method is shown. The results of the numerical and theoretical solutions coincide. The upshot of solving the two-dimensional problem by the right-hand side method is presented. The linearized Euler equations are numerically simulated. As in the one-dimensional case, good agreement between the exact and numerical solutions is obtained. The advantages of the method, which consist in saving computer time and resources, are outlined, the areas and directions of its use are determined.