Communications of the ACM · 1964 · 79 citations · 8 references
Natural SciencesComputational EngineeringComputational MechanicsComputational PhysicsDifferential EquationsBoundary ConditionsBoundary-value ProblemsFinite Difference MethodsNumerical AlgorithmsNumerical AnalysisNumerical Methods For Differential EquationsBoundary Value Problem SolversFinite Difference DiscretizationFinite Difference SchemesFinite Difference Solution Of Partial Differential EquationsNonlinear Boundary-value ProblemsNumerical Solutions Of Partial Differential EquationsTwo-point Boundary Value ProblemsTwo-point Boundary-value Formulation
Solution of nonlinear two-point boundary-value problems is often an extremely difficult task. Quite apart from questions of reality and uniqueness, there is no established numerical technique for this problem. At present, shooting techniques are the easiest method of attacking these problems. When these fail, the more difficult method of finite differences can often be used to obtain a solution. This paper gives examples and discusses the finite difference method for nonlinear two-point boundary-value problems.
8