Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Efficient Solution of Burgers’, Modified Burgers’ and KdV–Burgers’ Equations Using B-Spline Approximation Functions
View through CrossRef
This paper discusses the application of the orthogonal collocation on finite elements (OCFE) method using quadratic and cubic B-spline basis functions on partial differential equations. Collocation is performed at Gaussian points to obtain an optimal solution, hence the name orthogonal collocation. The method is used to solve various cases of Burgers’ equations, including the modified Burgers’ equation. The KdV–Burgers’ equation is considered as a test case for the OCFE method using cubic splines. The results compare favourably with existing results. The stability and convergence of the method are also given consideration. The method is unconditionally stable and second-order accurate in time and space.
Title: Efficient Solution of Burgers’, Modified Burgers’ and KdV–Burgers’ Equations Using B-Spline Approximation Functions
Description:
This paper discusses the application of the orthogonal collocation on finite elements (OCFE) method using quadratic and cubic B-spline basis functions on partial differential equations.
Collocation is performed at Gaussian points to obtain an optimal solution, hence the name orthogonal collocation.
The method is used to solve various cases of Burgers’ equations, including the modified Burgers’ equation.
The KdV–Burgers’ equation is considered as a test case for the OCFE method using cubic splines.
The results compare favourably with existing results.
The stability and convergence of the method are also given consideration.
The method is unconditionally stable and second-order accurate in time and space.
Related Results
Numerical Solution of Nonlinear Kaup-Kupershmit Equation, KdV-KdV and Hirota-Satsuma Systems
Numerical Solution of Nonlinear Kaup-Kupershmit Equation, KdV-KdV and Hirota-Satsuma Systems
Abstract
In this work we investigate the numerical solution of Kaup-Kupershmit (KK) equation, KdV-KdV and generalized Hirota-Satsuma (HS) systems. The proposed numer...
Extensive Experimental Study on the Stability of Rotor System With Spline Coupling
Extensive Experimental Study on the Stability of Rotor System With Spline Coupling
Spline couplings which have simple structure, high reliability and can compensate torque transmission error are widely used in rotating machineries, such as aeroengine and gasturbi...
the Solving Partial Differential Equations by using Efficient Hybrid Transform Iterative Method
the Solving Partial Differential Equations by using Efficient Hybrid Transform Iterative Method
The aim of this article is to propose an efficient hybrid transform iteration method that combines the homotopy perturbation approach, the variational iteration method, and the Abo...
Noncommutative Korteweg–de Vries and modified Korteweg–de Vries hierarchies via recursion methods
Noncommutative Korteweg–de Vries and modified Korteweg–de Vries hierarchies via recursion methods
Here, noncommutative hierarchies of nonlinear equations are studied. They represent a generalization to the operator level of corresponding hierarchies of scalar equations, which c...
Improving Deformable Multi-Grid B-spline Registration using Heuristics and Deep Learning
Improving Deformable Multi-Grid B-spline Registration using Heuristics and Deep Learning
The purpose of deformable image registration is to recover acceptable spatial transformations that align two images acquired at different periods of time into the same coordinate s...
Asymptotic attraction with algebraic rates toward fronts of dispersive–diffusive Burgers equations
Asymptotic attraction with algebraic rates toward fronts of dispersive–diffusive Burgers equations
Abstract
Burgers equation is a classic model, which arises in numerous applications. At its very core, it is a simple conservation law, which serves as a toy model for various d...
Procedure for Western blot v1
Procedure for Western blot v1
Goal: This document has the objective of standardizing the protocol for Western blot. This technique allows the detection of specific proteins separated on polyacrylamide gel and t...
Hawkins Omniversal Theory - 15 Hot-Modified Equations
Hawkins Omniversal Theory - 15 Hot-Modified Equations
Hawkins Omniversal Theory - (15) HOT-Modified EquationsThe Hawkins Omniversal Theory (HOT) - 15 Modified Equations presents a rigorously developed set of equations designed to addr...