Search

This paper proposes an accurate and robust meshless approach for the numerical solution of the nonlinear equal width equation. The numerical technique is applied for approximating the spatial variable derivatives of the model based on the localized radial basis function-finite difference (RBF-FD) method. Another implicit technique based on θ − weighted and finite difference methods is also employed for approximating the time variable derivatives. The stability analysis of the approach is demonstrated by employing the Von Neumann approach. Next, six test problems are solved including single solitary wave, fusion of two solitary waves, fusion of three solitary waves, soliton collision, undular bore, and the Maxwellian initial condition. Then, the L 2 and L ∞ norm errors for the first example and the I 1 , I 2 , and I 3 invariants for the other examples are calculated to assess accuracy of the method. Finally, the validity, efficiency and accuracy of the method are compared with those of other techniques in the literature. [ABSTRACT FROM AUTHOR]

The local radial basis function (LRBF) method is an excellent tool for solving variable-order time-fractional evolution equations. This method reduces the expensive computational cost of the conventional global RBF collocation (GRBFC) approach. The present paper represents an efficient mesh-less LRBF collocation approach for solving the two-dimensional (2D) fractional evolution equation for the arbitrary fractional order in complex-shaped domains. Having been used an appropriate finite difference (FD) technique to discrete the time variable, the LRBF method is applied in order to solve the equation. Unlike the conventional GRBFC method, consideration of the local nodes in a subdomain surrounding the given local point is needed for the proposed LRBF method. This method can reduce the ill-conditioning of the global resultant RBF interpolation matrix while it is also well efficient for large scale problems. Some illustrative examples are given to demonstrate the efficiency and proficiency of the method. [ABSTRACT FROM AUTHOR]

This article has been retracted: please see Elsevier Policy on Article Withdrawal (https://www.elsevier.com/about/policies/article-withdrawal).