Mathematical Methods in the Applied Sciences · 2023 · 10 citations · 42 references
Natural SciencesPhysicsComputational MechanicsDifferential EquationsFluid DynamicsBoundary-value ProblemsConvergence AnalysisNumerical AnalysisNumerical ConvergencePerturbation MethodsPerturbation TheoryBoundary Value Problem SolversConvergence For Singular SolutionsDifferential Equation SolversNumerical Methods For Integral EquationsPerturbation Of Boundary Value ProblemsPerturbation Of Nonlinear Differential EquationsSingular Perturbation AnalysisSingularly Perturbed Boundary Value Problems
In this paper, a promising technique based on the homotopy perturbation method for solving singular nonlinear system of boundary value problems (BVPs) is employed. The original singular system of BVPs is transformed into an equivalent system of integral equations to overcome the singular behavior at , and then, the recursive series for the solution is established. The mathematical formulation is further supported by conducting the convergence analysis of the recursive schemes. The accuracy of the proposed method is tested by comparing against the current variational iteration method using many standard examples. It is shown that the proposed method is more accurate and efficient than the existing method such as Chebyshev operational matrix method and variational iteration method.
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Homotopy perturbation technique
Ji‐Huan He · Computer Methods in Applied Mechanics and Engineering · 1999 · 3.5K citations
Homotopy perturbation method for solving boundary value problems
Ji‐Huan He · Physics Letters A · 2005 · 1.1K citations