Solution Procedure for Systems of Partial Dierential-Algebraic Equations by NHPM and Laplace-Padé Resummation
Brahim Benhammouda, Hector Vazquez-Leal, Arturo Sarmiento-Reyes
Journal of Advances in Mathematics and Computer Science · pp. 3202–3223 · Published 15 Sep 2014
10.9734/BJMCS/2014/12168Abstract
In this paper, we propose an ecient modication of a New Homotopy Perturbation Method (NHPM) to obtain approximate and exact analytical solutions of Partial Dierential-Algebraic Equations (PDAEs). The NHPM is rst applied to the PDAE to obtain the exact solution in convergent series form. To improve the solution obtained from NHPM's truncated series, a post-treatment combining Laplace transform and Pade approximant is proposed. This modied Laplace-Pade new homotopy perturbation method is shown to be eective and greatly improves NHPM's truncated series solutions in convergence rate, and often leads to the exact solution. Two problems are solved to demonstrate the eciency of the method; the rst one is a nonlinear index-one system with an integral term and the second one is a linear index-three system with variable coecients.
References (62)
- 1 A coupling method of a homotopy technique and a perturbation technique for non-linear problems [DOI]
- 2 Application of homotopy perturbation method to nonlinear wave equations [DOI]
- 3 Homotopy perturbation method for solving boundary value problems [DOI]
- 4 Essentials of Pade approximants
- 5 The homotopy perturbation method for nonlinear oscillators with discontinuities [DOI]
- 6 Homotopy Perturbation Method for Bifurcation of Nonlinear Problems [DOI]
- 7 The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods [DOI]
- 8 Approximate solution of nonlinear differential equations with convolution product nonlinearities [DOI]
- 9 Analytic approximate solutions for steady flow over a rotating disk in porous medium with heat transfer by homotopy analysis method [DOI]
- 10 Solutions of non-linear oscillators by the modified differential transform method [DOI]
- 11 An aftertreatment technique for improving the accuracy of Adomian's decomposition method [DOI]
- 12 Exact solutions of some coupled nonlinear partial differential equations using the homotopy perturbation method [DOI]
- 13 A STUDY OF NON-NEWTONIAN FLOW AND HEAT TRANSFER OVER A NON-ISOTHERMAL WEDGE USING THE HOMOTOPY ANALYSIS METHOD [DOI]
- 14 An approximate analytic solution of the nonlinear Riccati differential equation [DOI]
- 15 Nonlinear vibration of an electrostatically actuated microbeam [DOI]
- 16 A new homotopy perturbation method for solving systems of partial differential equations [DOI]
- 17 On the numerical solution of the model for HIV infection of CD4+ T cells [DOI]
- 18 The homotopy perturbation method for solving neutral functional–differential equations with proportional delays [DOI]
- 19 A Differentiation Index for Partial Differential-Algebraic Equations [DOI]
- 20 The modified homotopy perturbation method for solving strongly nonlinear oscillators [DOI]
- 21 Solving a model for the evolution of smoking habit in Spain with homotopy analysis method [DOI]
- 22 Solution of the differential algebraic equations via homotopy perturbation method and their engineering applications [DOI]
- 23 The modified algorithm for the differential transform method to solution of Genesio systems [DOI]
- 24 A reliable aftertreatment for improving the differential transformation method and its application to nonlinear oscillators with fractional nonlinearities [DOI]
- 25 Adomian decomposition method for solution of differential-algebraic equations [DOI]
- 26 Generalized homotopy method for solving nonlinear differential equations [DOI]
- 27 A General Solution for Troesch′s Problem [DOI]
- 28 Vibration of electrostatically actuated microbeam by means of homotopy perturbation method [DOI]
- 29 Convergence of Runge–Kutta methods applied to linear partial differential-algebraic equations [DOI]
- 30 Molten carbonate fuel cell (MCFC) with internal reforming: model-based analysis of cell dynamics [DOI]
- 31 Elliptic Partial Differential-Algebraic Multiphysics Models in Electrical Network Design [DOI]
- 32 An effective modification of the homotopy perturbation method for stiff systems of ordinary differential equations [DOI]
- 33 Parabolic Differential-Algebraic Models in Electrical Network Design [DOI]
- 34 Blow-up in a System of Partial Differential Equations with Conserved First Integral. Part II: Problems with Convection [DOI]
- 35 Application of Homotopy Perturbation Method for Fuzzy Linear Systems and Comparison with Adomian’s Decomposition Method [DOI]
- 36 Variational Methods for Solving Warped Multirate Partial Differential Algebraic Equations [DOI]
- 37 A method of characteristics for solving multirate partial differential equations in radio frequency application [DOI]
- 38 Modelling a flexible slider crank mechanism by a mixed system of DAEs and PDEs [DOI]
- 39 Arbitrary order numerical method for solving differential-algebraic equation by Padé series [DOI]
- 40 Solving system of DAEs by homotopy analysis method [DOI]
- 41 A Joint DAE/PDE Model for Interconnected Electrical Networks [DOI]
- 42 Discretization based indices for semilinear partial differential algebraic equations [DOI]
- 43 Perturbation index of linear partial differential-algebraic equations [DOI]
- 44 Homotopy perturbation method for linear programming problems [DOI]
- 45 A Concept for Classification of Partial Differential Algebraic Equations in Nanoelectronics [DOI]
- 46 A new technique for solving nonlinear integral–differential equations [DOI]
- 47 A further index concept for linear PDAEs of hyperbolic type [DOI]
- 48 A Numerical Method for Partial Differential Algebraic Equations Based on Differential Transform Method [DOI]
- 49 Indexes and Special Discretization Methods for Linear partial Differential Algebraic Equations [DOI]
- 50 Index Analysis of Multirate Partial Differential-Algebraic Systems in RF-Circuits [DOI]
- 51 Homotopy perturbation technique [DOI]
- 52 Application of He's Homotopy Perturbation Method to Volterra's Integro-differential Equation [DOI]
- 53 Variational iteration algorithm-II for solving linear and non-linear ODEs [DOI]
- 54 Solving system of DAEs by Modified Homotopy Perturbation Method [DOI]
- 55 Nonlinear Vibration of Electrostatically Actuated Microbeam [DOI]
- 56 Modified Homotopy Perturbation Method for nonlinear system of second-order BVPs [DOI]
- 57 Exact Solution for High-Order Integro-Differential Equations by NHPM
- 58 Modified Homotopy Perturbation Method for Dolving Nonlinear PDAEs and its Applications in Nanoelectronics [DOI]
- 59 Efficient Solution and Sensitivity Analysis of Partial Differential-Algebraic Equation Systems [DOI]
- 60 Solution of the nonlinear PDAEs by variational iteration method and its applications in nanoelectronics [DOI]
- 61 Index Concepts for Linear Mixed Systems of Differential-Algebraic and Hyperbolic-Type Equations [DOI]
- 62 Navier-Stokes equations as a differential-algebraic system
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