On boundary value problem for a differential equation with variant retarded argument
Applied Mathematics and Computation
Applied Mathematics and Computation
Multiple shooting method for two-point boundary value problems
Communications of the ACM
Multi-point boundary value problems for second-order functional differential equations
Computers & Mathematics with Applications
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A new numerical method for two-point boundary value problems associated to differential equations with deviating argument is obtained. The method uses the fixed point technique, the trapezoidal quadrature rule, and the cubic spline interpolation procedure. The convergence of the method is proved without smoothness conditions, the kernel function being Lipschitzian in each argument. The interpolation procedure is used only on the points where the argument is modified. A practical stopping criterion of the algorithm is obtained and the accuracy of the method is illustrated on some numerical examples of the pantograph type.