Research On Numerical Solution Of Second-order Matrix Differential Equations Using Matrix Splines Function

Spline are applied widely in function approximation, computational geometry,CAGD,wavelet,numerical solutions of differential equations and so on。This article discusses some applications of the matrix differential equations used by matrix spline function.Chapter 1: Introduce why we research matrix differential equations, basic knowledge of matrix differential equations with the initial values, and finally descript the matrix spline function.Chapter 2: Introduce the numerical solution of the first order matrix differential equations using matrix spline function, and mainly sum up the method of first order matrix differential equation using spline function in recent years, it is introduced with two parts. Section I describes the numerical solution of first order matrix linear differential equation using the cubic matrix spline function and quartic matrix spline function. Section II describes the numerical solution of first-order matrix differential non-linear equation using the cubic matrix spline function.Chapter 3: Introduce the numerical solution of the second order matrix differential using matrix spline function.Firstly,introduce the numerical solution of the second order matrix differential equations using cubic spline function, based on the anterior results ,present the constructions of the numerical solution of second order using matrix quartic spline;Secondly,design the algorithm of the application of the matrix cubic spline and the matrix quartic spline to approximate to the differential function;Thirdly,for the same linear matrix differential equation and non-linear matrix differential equation, respectively use the cubic spline and the quartic spline to approximate;Finally through a comparison of numerical error and error images, proves that the feasibility and effectiveness of the methods for the numerical solution of the matrix difference equations.Chapter 4: summarizes the whole dissertation and gives some expectation for future research.