[PDF] Top 20 Application of Homotopy Analysis Method for Solving Various Types of Problems of Partial Differential Equations

... of partial differential equations (PDEs) arise in many scientific models such as the propagation of shallow water waves and the Brusselator model of the chemical reaction-diffusion ...the ... See full document

... tional partial differential ...iteration method [– ], the Adomian descomposition method [, ], the fractional sub-equation method [–], the homotopy perturbation technique ... See full document

... decomposition method [2] was introduced, which is an exceptionally effective and powerful method for solving linear and nonlinear problems in various ...of problems with easy way ... See full document

... -expansion method [4] and Hirota bilinear method ...nonlinear partial diffenential equations by using various ...decomposition method (ADM) [7], He’s Semi- inverse method ... See full document

... engineering problems, there is a growing interest in exploring new methods to solve the equation more accurately and efficiently ...nonlinear partial differential equations by using ... See full document

... combined method for defining the field points and connected using optimization ...for application of Nonlinear FEM to non rigid motion ...of partial differential ...value problems whose ... See full document

... The homotopy analysis method (HAM) was proposed by ...this method, the solution is considered as the summation of an infinite series, which usually converges rapidly to the exact ...on ... See full document

... with homotopy analysis method is proposed to solve nonlinear fractional partial differential ...This method is called the fractional homotopy analysis natural ... See full document

... NTEGRO-DIFFERENTIAL equations arise in modeling various physical and engineering ...problems. Solving such equations is very interesting, and several numerical and analytical ... See full document

... the application of the homotopy perturbation method (HPM) [1, 7] in nonlinear problems has been developed by scientists and engineers, because this method continuously deforms the ... See full document

... Diverse problems of physical interest are described by both linear and nonlinear partial differential equations with initial and boundary ...nonlinear partial differential ... See full document

... governing differential equations do not have analytical solutions in genuine events in nature and ...afore-mentioned equations, the analytical solutions are not ...the homotopy perturbation ... See full document

... value problems occur in the study of fluid dynamics, astrophysics, hydrodynamic, hydro magnetic stability, astronomy, beam and long wave theory, induction motors, engineering, and applied ...value problems ... See full document

... nonlinear problems without any need for discretization and linearization as in numerical methods ...a method based on HPM for acquiring an approximate-analytical solution of the ...based method is ... See full document

... and analysis the linear and nonlinear optimal control ...decomposition method [1], homotopy Analysis method HAM [2], variational iteration method VIM [3] and homotopy ... See full document

... the homotopy analysis method is simi- lar to the Jacobi iterative ...the homotopy analysis method is D −1 b, while the initial value of the Jacobi iterative method is ... See full document

... decomposition method for solving nonlinear ordinary and partial differential equations, the same problems are solved by He-Laplace ...decomposition method provides the ... See full document

... solve equations in a discretized ...the equations of fluid motion (Euler equations, Navier-Stokes equations, ...subspace method or al- gorithms from Multigrid family are typically ... See full document

... mation equations during computation. For different types of problems, the derived orthonormal functions are dif- ferent, which are closely related to the solution expres- ... See full document

... the various mathematical methods of ...direct method of Hirota to obtain the multi-soliton solutions of physically significant nonlinear waves ...includes equations with single bilinear form and ... See full document