Communications in Applied Numerical Methods · 1985 · 11 citations · 7 references
EngineeringComputational EngineeringComputational MechanicsDifferential EquationsFinite Element MethodsBoundary ConditionsFinite Element FormulationFracture MechanicsNumerical AlgorithmsNumerical Methods For Differential EquationsSolid Mechanics ApplicationsComputational Fracture MechanicsMethod Of LinesNonlinear Partial Differential EquationsNonlinear SystemsNumerical Analysis Of Partial Differential EquationsNumerical SimulationNumerical Solutions Of Partial Differential EquationsSingular Boundary-value Problems
Abstract The recursive formulation of the Tau method of Ortiz 6 is a versatile tool for the numerical solution of linear and nonlinear systems of differential equations. In this paper it is combined with the method of lines to produce a hybrid Tau lines method which has been applied with success in the numerical treatment of partial differential equations. We report here results obtained in the numerical solution of the biharmonic equation and show that the Tau lines technique performs far better than a specially designed finite element method with which it is compared. We also report results obtained in the numerical solution of a singular boundary‐value problem, defined again by the biharmonic equation, which is relevant to fracture mechanics.
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