Use of New Residual Correction Method to Calculate Upper and Lower Solutions of Natural Convection

Abstract

This article uses the concept of differential equation maximum principle as well as the technique of virtual time to establish a solution's monotonic relation with the residual of a differential equation for a natural-convection problem. To obtain solutions, the article first uses cubic spline approximation to discretize the equation, then applies a new “residual correction method” to convert the once complex inequality constraint mathematical programming problem into a simple problem of equation iteration. The numerical results validate the correctness of this method. Moreover, when there are a very limited number of grid points, the accuracy of mean approximate solutions is still rather satisfying.

Thanks to National Science Council, the Republic of China, for the subsidy of Outlay 93-2212-E-432-001 to help us finish this special research successfully.