Mathematics of Computation · 1974 · 93 citations · 20 references
ComputingComputational EngineeringComputational Fluid DynamicsComputational PhysicsDifferential EquationsAdaptive Mesh RefinementConvergence AnalysisFinite Difference MethodsNumerical AlgorithmsNumerical ConvergenceNumerical Methods For Differential EquationsFinite Difference DiscretizationFinite Difference SchemesMesh ConvergenceMultipoint Boundary Value ProblemsNonlinear Boundary-value ProblemsNumerical Solutions Of Ordinary Differential Equations
An adaptive finite difference method for first order nonlinear systems of ordinary differential equations subject to multipoint nonlinear boundary conditions is presented. The method is based on a discretization studied earlier by H. B. Keller. Variable order is provided through deferred corrections, while a built-in natural asymptotic estimator is used to automatically refine the mesh in order to achieve a required tolerance. Extensive numerical experimentation and a FORTRAN program are included.
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