Optimal homotopy solution of the sine-Gordon equation
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Shivangi Dangi
Abstract
In this work, we obtain the series solution of the sine-Gordon equation with given initial conditions by the optimal homotopy analysis method (OHAM). The square residual error is calculated with respect to the associated independent parameters. The obtained solutions for three particular cases of the sine-Gordon equation are compared with the VIM and exact solutions wherever possible. The optimal OHAM solutions are more accurate in comparison to the variational iteration method (VIM).
Abstract
In this work, we obtain the series solution of the sine-Gordon equation with given initial conditions by the optimal homotopy analysis method (OHAM). The square residual error is calculated with respect to the associated independent parameters. The obtained solutions for three particular cases of the sine-Gordon equation are compared with the VIM and exact solutions wherever possible. The optimal OHAM solutions are more accurate in comparison to the variational iteration method (VIM).
Chapters in this book
- Frontmatter I
- Contents V
- Fixed points and their geometric properties for interpolative contravariant mappings 1
- Coupled fixed point theorems for F-contraction mappings in S-metric spaces 15
-
Fixed point theorems in convex
- Image formulae for the Saigo fractional q-derivative operator with basic hypergeometric series 55
- A result on solvability for a class of nonlinear fractional integral equations in a Banach space 73
- Solvability of Hadamard fractional integral equations via fixed point theorem 87
- Improved pseudospectral approximation for nonlinear parabolic equation 99
-
Analysis of atmospheric
- A numerical scheme based on Galerkin method for solving singularly perturbed differential equation with mixed shifts 127
- Influence of urbanization and climate change on the human population through a mathematical modeling 143
- Effect of preservation on an EPQ model with selling and credit period-dependent demand under carbon tax policy 157
- Optimal homotopy solution of the sine-Gordon equation 175
- Significance of chemical interactions and thermal transpiration on transient MHD-free convective heat and mass transport over an infinite plate via porous media 191
Chapters in this book
- Frontmatter I
- Contents V
- Fixed points and their geometric properties for interpolative contravariant mappings 1
- Coupled fixed point theorems for F-contraction mappings in S-metric spaces 15
-
Fixed point theorems in convex
- Image formulae for the Saigo fractional q-derivative operator with basic hypergeometric series 55
- A result on solvability for a class of nonlinear fractional integral equations in a Banach space 73
- Solvability of Hadamard fractional integral equations via fixed point theorem 87
- Improved pseudospectral approximation for nonlinear parabolic equation 99
-
Analysis of atmospheric
- A numerical scheme based on Galerkin method for solving singularly perturbed differential equation with mixed shifts 127
- Influence of urbanization and climate change on the human population through a mathematical modeling 143
- Effect of preservation on an EPQ model with selling and credit period-dependent demand under carbon tax policy 157
- Optimal homotopy solution of the sine-Gordon equation 175
- Significance of chemical interactions and thermal transpiration on transient MHD-free convective heat and mass transport over an infinite plate via porous media 191
