B‐spline collocation algorithm for numerical solution of the generalized Burger's‐Huxley equation

Abstract

The cubic B‐spline collocation scheme is implemented to find numerical solution of the generalized Burger's–Huxley equation. The scheme is based on the finite‐difference formulation for time integration and cubic B‐spline functions for space integration. Convergence of the scheme is discussed through standard convergence analysis. The proposed scheme is of second‐order convergent. The accuracy of the proposed method is demonstrated by four test problems. The numerical results are found to be in good agreement with the exact solutions. Results are compared with other results given in literature. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013

Quintic trigonometric spline based numerical scheme for nonlinear modified Burgers' equation

“…The convergence of the scheme is established using some standard analysis procedures. The method used in is adopted in this paper. The following lemma is utilized to study the convergence of the scheme.Lemma The quintic trigonometric B‐splines TB −2 , TB −1 , TB 0 , …, TB N+1 , TB N+2 satisfy the inequality where α 1 = TB m−2 (x) = TB m+2 (x), α 2 = TB m−1 (x) = TB m+1 (x) and α 3 = TB m (x). Proof At any node x m , from the quintic trigonometric B‐spline formulation, we have | TB m −2 ( x )| = | α 1 |, | TB m −1 ( x )| = | α 2 |, | TB m ( x )| = α 3 , | TB m +1 ( x )| = α 2 , | TB m +2 ( x )| = | α 1 |.…”

“…The convergence of the scheme is established using some standard analysis procedures. The method used in [46] is adopted in this paper. The following lemma is utilized to study the convergence of the scheme.…”

Strang splitting method for Burgers–Huxley equation

“…The resulting nonlinear system is solved by predictorcorrector method. A higher order finite difference scheme [16] and B-spline collocation scheme [17] are implemented to find numerical solution of the generalized BHE.…”

A New Numerical Algorithm for Solving a Class of Fractional Advection-Dispersion Equation with Variable Coefficients Using Jacobi Polynomials

“…Spectral collocation method has an exponential convergence rate, which is valuable in providing highly accurate solutions to nonlinear differential equations even using a small number of grids. Moreover, the choice of collocation points is very useful for the convergence and efficiency of the collocation approximation [7,8].…”