Applying the differential equation maximum principle with cubic spline method to determine the error bounds of forced convection problems

This article uses the concept of differential equation maximum principle as well as the technique of virtual time to establish the solution's monotonic relation with residual of forced convection. To obtain error bounds of approximate solution, the article first uses cubic spline approximation to discretize the differential equation, then applies “residual correction method” newly put forth by it to convert the once complex inequation constraint mathematical programming problem into a simple problem of equation iteration. What is more, not only the obtained upper and lower approximate solutions of the differential equation can correctly analyze error range, but also it is found that the new method helps increase the accuracy of mean approximate solutions.