Zeitschrift für Naturforschung A · 2009 · 201 citations · 1 references
Natural SciencesPhysicsComputational MechanicsDifferential EquationsFluid DynamicsBoundary ConditionsBoundary-value ProblemsNumerical AnalysisNumerical Methods For Differential EquationsPartial Differential EquationsPerturbation MethodsAccuracyNonlinear Boundary-value ProblemsNonlinear Partial Differential EquationsNumerical Analysis Of Partial Differential EquationsNumerical Solutions Of Partial Differential EquationsParabolic Partial Differential EquationsPartial Differential Equation SolversPerturbation Of Boundary Value Problems
Abstract In this work, the homotopy perturbation method proposed by Ji-Huan He [1] is applied to solve both linear and nonlinear boundary value problems for fourth-order partial differential equations. The numerical results obtained with minimum amount of computation are compared with the exact solution to show the efficiency of the method. The results show that the homotopy perturbation method is of high accuracy and efficient for solving the fourth-order parabolic partial differential equation with variable coefficients. The results show also that the introduced method is a powerful tool for solving the fourth-order parabolic partial differential equations.
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