EXACT SOLUTION OF SOME LINEAR AND NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS BY LAPLACE-ADOMIAN METHOD AND SBA METHOD

In this paper, a novel analytical method for solving nonlinear partial differential equations is studied. This method is known as triple Laplace transform decomposition method. This method is generalized in the sense of conformable derivative. Important results and theorems concerning this method are discussed. A new algorithm is proposed to solve linear and nonlinear partial differential equations in three dimensions. Moreover, some examples are provided to verify the performance of the proposed algorithm. This method presents a wide applicability to solve nonlinear partial differential equations in the sense of conformable derivative.

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Solution Non Linear Partial Differential Equations By ZMA Decomposition Method

WSEAS TRANSACTIONS ON MATHEMATICS ◽

10.37394/23206.2021.20.75 ◽

2021 ◽

Vol 20 ◽

pp. 712-716

Author(s):

Zainab Mohammed Alwan

Keyword(s):

Exact Solution ◽

Partial Differential Equations ◽

Differential Equations ◽

Decomposition Method ◽

Integral Transformation ◽

Nonlinear Partial Differential Equations ◽

Adomian Decomposition Method ◽

Partial Differential ◽

Linear Partial Differential Equations ◽

Adomian Decomposition

In this survey, viewed integral transformation (IT) combined with Adomian decomposition method (ADM) as ZMA- transform (ZMAT) coupled with (ADM) in which said ZMA decomposition method has been utilized to solve nonlinear partial differential equations (NPDE's).This work is very useful for finding the exact solution of (NPDE's) and this result is more accurate obtained with compared the exact solution obtained in the literature.

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Continuous Solution of Partial Differential Equations on Non-Rectangular and Non-Continuous Geometry

Volume 1A: 34th Computers and Information in Engineering Conference ◽

10.1115/detc2014-35148 ◽

2014 ◽

Author(s):

P. Venkataraman

Keyword(s):

Finite Element ◽

Partial Differential Equations ◽

Differential Equations ◽

Continuous Solution ◽

Finite Difference Methods ◽

Nonlinear Partial Differential Equations ◽

Partial Differential ◽

Mesh Free ◽

Numeric Calculation ◽

Linear And Nonlinear

A high order continuous solution is obtained for partial differential equations on non-rectangular and non-continuous domain using Bézier functions. This is a mesh free alternative to finite element or finite difference methods that are normally used to solve such problems. The problem is handled without any transformation and the setup is direct, simple, and involves minimizing the error in the residuals of the differential equations along with the error in the boundary conditions over the domain. The solution can be expressed in polynomial form. The effort is same for linear and nonlinear partial differential equations. The procedure is developed as a combination of symbolic and numeric calculation. The solution is obtained through the application of standard unconstrained optimization. A constrained approach is also developed for nonlinear partial differential equations. Examples include linear and nonlinear partial differential equations. The solution for linear partial differential equations is compared to finite element solutions from COMSOL.

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