scholarly journals Local extreme learning machines and domain decomposition for solving linear and nonlinear partial differential equations

2021 ◽  
Vol 387 ◽  
pp. 114129
Author(s):  
Suchuan Dong ◽  
Zongwei Li
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Domain Decomposition ◽  
Nonlinear Partial Differential Equations ◽  
Extreme Learning Machines ◽  
Partial Differential ◽  
Learning Machines ◽  
Linear And Nonlinear ◽  
Local Extreme

scholarly journals Analytical Solutions for the Nonlinear Partial Differential Equations Using the Conformable Triple Laplace Transform Decomposition Method

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Shailesh A. Bhanotar ◽  
Mohammed K. A. Kaabar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Laplace Transform ◽  
Analytical Solutions ◽  
Decomposition Method ◽  
Nonlinear Partial Differential Equations ◽  
Three Dimensions ◽  
Conformable Derivative ◽  
Partial Differential ◽  
Linear And Nonlinear

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.

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

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.

scholarly journals He-Laplace Method for Linear and Nonlinear Partial Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
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.

Sign in / Sign up

Export Citation Format

Share Document