Parallel Laplace Method with Assured Accuracy for Solutions of Differential Equations by Symbolic Computations

Lump-type solutions, rationally localized in many directions in the space, are analyzed for nonlinear differential equations derived from generalized bilinear differential equations. By symbolic computations with Maple, positive quadratic and quartic polynomial solutions to two classes of generalized bilinear differential equations on [Formula: see text] are computed, and thus, lump-type solutions are presented to the corresponding nonlinear differential equations on [Formula: see text], generated from taking a transformation of dependent variables [Formula: see text].

Download Full-text

He-Laplace Method for Linear and Nonlinear Partial Differential Equations

Journal of Applied Mathematics ◽

10.1155/2012/180315 ◽

2012 ◽

Vol 2012 ◽

pp. 1-16 ◽

Cited By ~ 13

Author(s):

Hradyesh Kumar Mishra ◽

Atulya K. Nagar

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Perturbation Method ◽

Homotopy Perturbation Method ◽

Nonlinear Partial Differential Equations ◽

Laplace Method ◽

Partial Differential ◽

Homotopy Perturbation ◽

Linear And Nonlinear ◽

New Treatment

A new treatment for homotopy perturbation method is introduced. The new treatment is called He-Laplace method which is the coupling of the Laplace transform and the homotopy perturbation method using He’s polynomials. The nonlinear terms can be easily handled by the use of He’s polynomials. The method is implemented on linear and nonlinear partial differential equations. It is found that the proposed scheme provides the solution without any discretization or restrictive assumptions and avoids the round-off errors.

Download Full-text

Analysis of fractional duffing oscillator

Revista Mexicana de Física ◽

10.31349/revmexfis.66.187 ◽

2020 ◽

Vol 66 (2 Mar-Apr) ◽

pp. 187 ◽

Cited By ~ 1

Author(s):

S.C. Eze

Keyword(s):

General Solution ◽

Differential Equations ◽

Perturbation Method ◽

Fractional Differential Equations ◽

Analytical Method ◽

Duffing Oscillator ◽

Laplace Method ◽

Nonlinear Fractional Differential Equations ◽

Non Linear ◽

Fractional Differential

In this contribution, a simple analytical method (which is an elegant combination of a well known methods; perturbation method and Laplace method) for solving non-linear and non-homogeneous fractional diﬀerential equations is pro- posed. In particular, the proposed method was used to analysed the fractional Duﬃng oscillator.The technique employed in this method can be used to analyse other nonlinear fractional diﬀerential equations, and can also be extended to non- linear partial fractional diﬀerential equations.The performance of this method is reliable, eﬀective and gives more general solution.

Download Full-text