Solving Differential Equations Using Modified Picard Iteration

Autor/in	Robin, W. A.
Titel	Solving Differential Equations Using Modified Picard Iteration
Quelle	In: International Journal of Mathematical Education in Science and Technology, 41 (2010) 5, S. 649-665Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0020-739X
Schlagwörter	Forschungsbericht; Equations (Mathematics); Computation; Teaching Methods; Problem Solving; Mathematics Instruction; Computer Uses in Education; Educational Technology; Computer Software + Suchen Sie Ihr Suchwort? Equations; Mathematics; Gleichungslehre; Teaching method; Lehrmethode; Unterrichtsmethode; Problemlösen; Mathematics lessons; Mathematikunterricht; Computernutzung; Unterrichtsmedien
Abstract	Many classes of differential equations are shown to be open to solution through a method involving a combination of a direct integration approach with suitably modified Picard iterative procedures. The classes of differential equations considered include typical initial value, boundary value and eigenvalue problems arising in physics and engineering and include non-linear as well as linear differential equations. Examples involving partial as well as ordinary differential equations are presented. The method is easy to implement on a computer and the solutions so obtained are essentially power series. With its conceptual clarity (differential equations are integrated "directly"), its uniform methodology (the "overall" approach is the same in all cases) and its straightforward computer implementation (the integration and iteration procedures require only standard commercial software), the modified Picard methods offer obvious benefits for the teaching of differential equations as well as presenting a basic but flexible tool-kit for the solution process itself. (As Provided).
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Begutachtung	Peer reviewed
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10