An efficient numerical method for solving coupled Burgers' equation by combining homotopy perturbation and pade techniques

Abstract

In this study, we combined homotopy perturbation and Pade techniques for solving homogeneous and inhomogeneous two-dimensional parabolic equation. Also, we apply our combined method for coupled Burgers' equations. The numerical results demonstrate that our combined method gives the approximate solution with faster convergence rate and higher accuracy than using the classic homotopy perturbation method.

Approximate Solutions for Flow with a Stretching Boundary due to Partial Slip

“…We observe that even though the series has a finite region of convergence, Padé approximant allows obtaining the limit of the function under study as x takes large values, if L = M (see Figures 3 and 5 ) [ 55 ]. In fact, the rational functions whose denominator and numerator have the same values of L and M , or a degree almost identical, give rise to results better than those obtained by methods based on polynomial functions [ 61 ].…”

“…Finally, the convergence is uniform in any compact region in the case of Padé approximation, whereas truncated Maclaurin series is valid only in a near neighbourhood of zero point. The above explains why HPM-Padé has larger intervals of convergence in comparison with HPM series [ 55 ].…”

Solution of the Coupled Burgers Equation Based on Operational Matrices of d-Dimensional Orthogonal Functions

“…In this example, we consider the two-dimensional linear homogeneous Burgers equation given by [12,13] g( with boundary conditions…”

“…By assuming u(x,t) = A T Φ(x,t) and v(x,t) = B T Φ(x,t) and applying the proposed method, (13) and (14) are obtained as…”

Chebyshev Wavelet Method for Numerical Solutions of Coupled Burgers Equation

“…Siraj-ul-Islam et al [17] solved coupled Burgers' equation by mesh free interpolation method. Kelleci and Yıldırım [20] have solved the equation by combining homotopy perturbation and Pade techniques and Inan et al [16] have applied Bäcklund transformation to the Eqs. (…”