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second order; difference operator; second order convergence; asymptotic expansion; global discretization error; numerical examples; boundary value problem; deviating argument; Richardson extrapolation; convergence of higher order
A numerical method for the solution of a second order boundary value problem for differential equation with state dependent deviating argument is studied. Second-order convergence is established and a theorem about the asymptotic expansion of global discretization error is given. This theorem makes it possible to improve the accuracy of the numerical solution by using Richardson extrapolation which results in a convergent method of order three. This is in contrast to boundary value problems for ordinary differential equations where the use of Richardson extrapolation results in a method of order four.
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