Nps Solution For Two Classes Of Ordinary Differential Equation Of Bvp Method Research

It is a pop topic in the recent that scientists research and apply the solution of Obstacle boundary value problem and Two-point boundary value problem that are two kinds of ordinary differential equations. There are a lot of numeric solutions. For example, Polynomial Spline solution method, Nonpolynomial Spline solution method, colloc-quintic method, B-spline method, Finite difference method and so on.In the paper, we construct the new function which include exponential function, trigonometric function and polynomial function by choosing different spline functions, and the class of function is span{1,x,x2, sin kx,ekx}.The new nonpolynomial spline function is continuously differentiable, second derivative of which is continuous. We can proof that the numeric solution to ordinary differential equations is feasibility by using related basic theories. We use the new nonpolynomial function respectively to approach the solutions of the boundary value problem of the two kinds of different ordinary differential equations. One is the obstacle boundary value problem; the other is two-point boundary value problem. Since the new nonpolynomial function and its derivative are continuous in knots, so we can deduce equations of the numeric solution to solute the two kinds of ordinary differential equations. Then we give the error analysis of the problem. The result shows that its local truncation error of the numeric solution is O(h6) by using Taylor expansion formula, and we can proof that the solution of the problem is second convergence. In the paper, we give some corresponding examples to solute numerically boundary value problems of the two kinds of ordinary differential equations, and the absolute errors are found by using a Matlab program, at last we give the maximum errors table. We discuss the different situations of the error in different basises. Compared to some present numeric solutions, such as cubic spline function and Finite difference method, the result shows that the approximation effect of the new numeric solution in the paper is better than the present method. At last, the error analysis pictures are given on the different step size to present more clearly good approximation effect and good precision.