Mathematical Methods in the Applied Sciences · 2011 · 15 citations · 15 references
Natural SciencesPhysicsComputational MechanicsComputational PhysicsDifferential EquationsConvergence AnalysisIntegral EquationsNumerical AnalysisNumerical ConvergenceNumerical IntegrationNumerical Methods For Differential EquationsAccuracyConvergenceDifferential Equation SolversNumerical Analysis Of Partial Differential EquationsNumerical Methods For Integral EquationsRegion Of Convergence
This paper presents general framework for solving the nth-order integro-differential equation using homotopy analysis method (HAM) and optimal homotopy asymptotic method (OHAM). OHAM is parameter free and can provide better accuracy over the HAM at the same order of approximation. Furthermore, in OHAM the convergence region can be easily adjusted and controlled. Comparison, via two examples, between our solution using HAM and OHAM and the exact solution shows that the HAM and the OHAM are effective and accurate in solving the nth-order integro-differential equation. Copyright © 2011 John Wiley & Sons, Ltd.
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