Numerical method for nonlinear differential equation with arbitrary BC: Numerical method for nonlinear differential equation - Softcover

Yahiaoui, Toufik

Softcover

ISBN 10: 6205512203 ISBN 13: 9786205512203

Verlag: LAP LAMBERT Academic Publishing, 2022

Inhaltsangabe

The aim of this work consists in developing an algorithm and a numerical calculation program allowing to solving a nonlinear arbitrary 2nd and 3rd order differential equation (DE) of with generalized Cauchy boundary conditions (BC) over the interval [a1, a2]. The Dirichlet and Neumann BC becomes a particular case. The problem consists in transforming the DE to a system of n(n+1) nonlinear DE of the first order (FODE) with initial n conditions (IC), of which n equations justify the function y(x) and these (n-1) successive derivatives, and of n2 functions again witch justify the transformation of the DE towards a system of FODE with IC. The number n is the order of the DE. The resolution of this system of equations is made by the adaptation of the Runge Kutta method of order 4. The determination of the IC is made by the resolution of an algebraic system of n nonlinear equations, of which the resolution is made simultaneously by the Newton's method. For each iteration of Newton’s method, a system of nonlinear algebraic equations is obtained whose solution is made by the method of Gauss.

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Über die Autorin bzw. den Autor

Dr Toufik Yahiaoui is a researcher at the Institute of Aeronautics and Space Studies of the University of Blida 1 in Algeria. He obtained the degree of State Doctorate in Aeronautics in 2007 and the rank of Professor in 2012. He has published more than 80 publications in journals and a dozen of scientific books.

Details zur Ausgabe

• Verlag: LAP LAMBERT Academic Publishing
• Erscheinungsdatum: 2022
• Sprache: Englisch
• ISBN 10: 6205512203
• ISBN 13: 9786205512203
• Einband: Taschenbuch
• Anzahl der Seiten: 72
• Kontakt zum Hersteller: Nicht verfügbar
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