Layered optimization algorithm about a kind of nonlinear partial differential equation with initial-boundary value problem

Abstract

For non-linear partial differential equations with initial-boundary value problems, based on the difference method and the optimization method with dynamic design variables, using unknown function values on discrete node points on time layer as design variables, the difference equations sets of all the discrete node points are constructed as stylized objective function. A layered accurate optimization algorithm about computing unknown function value on discrete node point is proposed. Universal computing program is designed, and practical examples are analyzed. Through comparing computation results with exact results, the effectiveness and the feasibility of proposed method are verified. The method can provide the condition for engineering application.