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.
Splainiais sudaromų nereguliariųjų matricų metodų taikymas paprastųjų diferencialinių lygčių kraštiniams uždaviniams spręsti
Darbe nagrinėjamas paprastųjų lygčių su kraštinėmis sąlygomis skaitinis sprendimo metodas. Šio metodo pagrindą sudaro nereguliariųjų matricų bei splainų konstravimas klasikiniu ortogonaliųjų polinomų pavidalu. Nagrinėjamo straipsnyje metodo taikymo galimybės parodytos įvairiais pavyzdžiais.
First Published Online: 14 Oct 2010
Keywords:
boundary values problems of ODE, splines, Degenerate Matrix method, differentiation matrix, zeroes of classical orthogonal polynomialsHow to Cite
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Copyright (c) 2005 The Author(s). Published by Vilnius Gediminas Technical University.
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Copyright (c) 2005 The Author(s). Published by Vilnius Gediminas Technical University.
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This work is licensed under a Creative Commons Attribution 4.0 International License.