Research Of Numerical Solutions Of Differential Equations Based On Spline Functions

The spline function is an important tool to make research for functionapproximation, as to differential equations, it introduces the numerical methods on the aclass of non-polynomial spline space and spline space on the uniform two-typetriangulation.As to the numerical solution of ordinary differential equations, it analyses anddiscusses the cubic spline functions in solving boundary value problem, it discusses aclass of non-polynomial spline makes difference method to solve boundary valueproblem, it proves the effectiveness of this type of non-polynomial spline differencemethod by the error estimates. It solves numerical solution of partial differentialequations by slice different degree quartic splineS₄^2,3(Δ_mn²)and slice six splineS₆⁴Δ_mn²)gives the numerical method and makes error analysis with examples to provethe effectiveness of the two spline methods. In the control numerical experimentbetween slice six spline and quintic spline method, it proves slice six spline method hashigher accuracy.