MULTIPOINT MOVING NODES FOR P ARABOLIC EQUATIONS
Abstract
This word discusses approximate solutions of linear parabolic equations with initial-boundary conditions. The primary focus is on methods that effectively find such solutions by employing a moving finite difference analog of the differential equation. This approach allows us to formulate an approximate analytical solution, significantly simplifying the computation process. By transitioning from the differential equation to an algebraic equation, we obtain a single equation, the solution of which represents an approximate analytical solution to the original problem. However, to achieve higher accuracy in this solution, we apply additional moving nodes, which enhances the results. By using multipoint moving nodes, we can form a system of algebraic equations, the solution of which provides us with an improved analytical solution. The article also presents numerical experiments that confirm the effectiveness of the proposed method and its advantages over traditional approaches.