Degenerate matrices methods by splines for boundary values problems of ordinary differential equations

Abstract

A method for numerical solving of boundary values problems of ordinary differential equations based on the use of splines and differentiation matrices with nodes as zeroes of classical orthogonal polynomials is considered. Possibilities of the method are shown by means of different examples. The method essentially uses the results obtained by Degenerate Matrices methods and it is applied for solving initial values problems of ordinary differential equations.

Darbe nagrinejamas paprastuju lygčiu su kraštinemis salygomis skaitinis sprendimo metodas. Šio metodo pagrinda sudaro nereguliariuju matricu bei splainu konstravimas klasikiniu ortogonaliuju polinomu pavidalu. Nagrinejamo straipsnyje metodo taikymo galimybes parodytos ivairiais pavyzdžiais.

Key words:

• boundary values problems of ODE
• splines
• Degenerate Matrix method
• differentiation matrix
• zeroes of classical orthogonal polynomials