Numerical method for nonlinear differential equation with arbitrary BC
Toufik Yahiaoui
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Numerical method for nonlinear differential equation with arbitrary BC

Numerical method for nonlinear differential equation

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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 o...