Moving Node Method for Differential Equations

Abstract

The chapter contains information about new approaches to solving boundary value problems for differential equations. It introduces a new method of moving nodes. Based on the approximation of differential equations (by the finite difference method or the control volume method), introducing the concept of a moving node, approximately analytical solutions are obtained. To increase the accuracy of the obtained analytical solutions, multipoint moving nodes are used. The moving node method is used to construct compact circuits. The moving node method allows you to investigate the diskette equation for monotonicity, as well as the approximation error of the differential equation. Various test problems are considered.

Obtaining Approximate Solutions of Differential Equations Using the Method of Moving Nodes

“…Analytical methods have a relatively low degree of universality for solving such problems. More universal are approximate analytical methods (projection, variational methods, small parameter methods, operational methods, and various iterative methods) [4][5][6][7].…”