Journal of Heat Transfer · 1982 · 19 citations · 3 references
ComputingComputational EngineeringMathematicsDifferential EquationsFinite Element AnalysisFinite Element MethodsFinite Difference MethodsFinite Element DiscretizationFinite Element FormulationNumerical AlgorithmsNumerical AnalysisNumerical Methods For Differential EquationsDiscretization Of Partial Differential EquationsFinite Difference DiscretizationFinite Difference SchemesFinite Difference Solution Of Partial Differential EquationsLinear Partial Differential EquationsNumerical Analysis Of Partial Differential EquationsNumerical Solutions Of Partial Differential EquationsPartial Differential Equation Solvers
A new method is proposed for obtaining finite difference equations for the solution of linear partial differential equations. The method is based on representing the approximate solution locally on a mesh element by polynomials which satisfy the differential equation. Then, by collocation, the value of the approximate solution, and its derivatives at the center of the mesh element may be expressed as a linear combination of neighbouring values of the solution.
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<i>Approximate Methods of Higher Analysis</i>
L. V. Kantorovich, V. I. Krylov, Curtis D. Benster et al. · Physics Today · 1960 · 1.5K citations