Piecewise homotopy analysis method and convergence analysis for formally well-posed initial value problems

Wang, Zhen; Zou, Li; Qin, Yupeng

doi:10.1007/s11075-017-0262-8

Cited by 3 publications

(1 citation statement)

References 16 publications

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“…The approximation should gain accuracy as we increase the total number of terms included in this expansion. Theorems concerning the convergence of the series to the true solution of the initial equation can be found in [1,3,[28][29][30][31][32][33][34][35].…”

Section: Homotopy Analysis Methods and Control Of Residual Error For Tmentioning

confidence: 99%

Optimal homotopy analysis and control of error for implicitly defined fully nonlinear differential equations

Gorder

2018

Numer Algor

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Implicitly defined fully nonlinear differential equations can admit solutions which have only finitely many derivatives, making their solution via analytical or numerical techniques challenging. We apply the optimal homotopy analysis method (OHAM) to the solution of implicitly defined ordinary differential equations, obtaining solutions with low error after few iterations or even one iteration of the method. This is particularly true in cases where an auxiliary nonlinear operator was employed (in contrast to the commonly used choice of an auxiliary linear operator), highlighting the need for further study on using auxiliary nonlinear operators in the HAM. Through various examples, we demonstrate that the approach is efficient for an appropriate selection of auxiliary operator and convergence control parameter.

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Section: Homotopy Analysis Methods and Control Of Residual Error For Tmentioning

confidence: 99%

Optimal homotopy analysis and control of error for implicitly defined fully nonlinear differential equations

Gorder

2018

Numer Algor

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Piecewise Jacobi–Picard Iteration Method for Solving Nonlinear Initial Value Problems on Large Domains

Tafakkori-Bafghi

Loghmani

Heydari

et al. 2022

Iran J Sci Technol Trans Sci

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Homotopy perturbation method for solving time-fractional nonlinear Variable-Order Delay Partial Differential Equations

Farhood¹,

Mohammed²

2023

Partial Differential Equations in Applied Mathematics

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Piecewise homotopy analysis method and convergence analysis for formally well-posed initial value problems

Cited by 3 publications

References 16 publications

Optimal homotopy analysis and control of error for implicitly defined fully nonlinear differential equations

Optimal homotopy analysis and control of error for implicitly defined fully nonlinear differential equations

Piecewise Jacobi–Picard Iteration Method for Solving Nonlinear Initial Value Problems on Large Domains

Homotopy perturbation method for solving time-fractional nonlinear Variable-Order Delay Partial Differential Equations

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