Proceedings of the Royal Society of London Series A Containing Papers of a Mathematical and Physical Character · 1910 · 325 citations · 0 references
Natural SciencesCivil EngineeringMathematicsComputational MechanicsDifferential EquationsStructural EngineeringBoundary ConditionsBoundary-value ProblemsFinite Difference MethodsIntegral EquationsNumerical AnalysisNumerical Methods For Differential EquationsBoundary Condition ApproximationBoundary Condition TreatmentBoundary Integral EquationsFinite Difference AnalysisFinite Difference ApproximationFinite Difference DiscretizationFinite Difference SchemesNumerical Methods For Integral Equations
Abstract In order to deal with irregular boundaries, analysis is replaced by arithmetic, continuous functions are represented by tables of numbers, differentials by central differences. Problems then fall into two classes:— (A) The relation between the equation obtaining throughout the body, and the boundary condition is such that the integral can be stepped out from a boundary. This class includes equations of all orders and degrees. It has been treated by arithmetical differences by Runge, W. F. Sheppard, Karl Heun, W. Kutta, and Richard Ganz. Examples of a specially simple method are given.