Improved pseudospectral approximation for nonlinear parabolic equation
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Harvindra Singh
Abstract
This study addresses the persistent challenge of nonlinear equations in various scientific fields by presenting an efficient solution to the nonlinear parabolic (Burgers) equation. We employ a collocation-based Chebyshev spectral method, utilizing the Chebyshev Gauss–Lobatto (CGL) points, to approximate the equation. By discretization, the original nonlinear equation is transformed into a system of ordinary differential equations (ODEs), which is solved using the fourth-order Runge–Kutta method. Our numerical experiments illustrate the superior effectiveness and robustness of our approach compared to existing methods. This methodology offers a promising solution for tackling nonlinear equations and provides a versatile framework applicable across diverse scientific domains.
Abstract
This study addresses the persistent challenge of nonlinear equations in various scientific fields by presenting an efficient solution to the nonlinear parabolic (Burgers) equation. We employ a collocation-based Chebyshev spectral method, utilizing the Chebyshev Gauss–Lobatto (CGL) points, to approximate the equation. By discretization, the original nonlinear equation is transformed into a system of ordinary differential equations (ODEs), which is solved using the fourth-order Runge–Kutta method. Our numerical experiments illustrate the superior effectiveness and robustness of our approach compared to existing methods. This methodology offers a promising solution for tackling nonlinear equations and provides a versatile framework applicable across diverse scientific domains.
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
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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
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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
