The numerical solution of boundary value problems for second order functional differential equations by finite differences

AbstractThe boundary value problem $$\ddot x(t) = g(t,x(t)) + (\mathfrak{F}x)(t)$$ , 0 <t < 1,x(0)=x(1)=0, is considered. Hereg:R2→R1 andF:C[0, 1] →C[0, 1]. The solutionx is approximated using finite differences. For a large class of problems it is proved that the approximate solutions exist and converge tox. The method is illustrated by the numerical example.

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