Quartic B-spline Galerkin approach to the numerical solution of the KdVB equation

The nonlinear Korteweg-de Vries-Burgers' equation is solved numerically by method of Galerkin using quartic B-splines as both shape and weight functions over the finite intervals. Five test problems are studied to demonstrate the accuracy and efficiency of the proposed method. A comparison of numerical results of both algorithm and some published articles is done in computational section. The numerical results are found in good agreement with exact solutions. (C) 2009 Elsevier Inc. All rights reserved

A numerical solution of the RLW equation by Galerkin method using quartic B-splines

Galerkin finite element method based on quartic B-splines is used to find a numerical solution of the regularized long wave equation. The method is tested on the problems of propagation of solitary waves, interaction of two and three solitary waves, undulation and wave generation. Comparisons are made with both analytical solutions and results of some published methods. Accuracy and efficiency of' the scherne are discussed by computing numerical conserved laws and L-2, L-infinity error norins. Copyright (C) 2007 John Wiley & Sons, Ltd

Parameter extraction for photovoltaic models with tree seed algorithm

Evaluation, simulation and optimization of PV systems is very important for fast and accurate parameter extraction based on current–voltage and power–voltage characteristic curves of photovoltaic models. Therefore, researchers used many metaheuristic algorithms to estimate the parameters of various PV modules. In this study, tree seed algorithm (TSA) was used for parameter estimation of the STM6-40/36 PV module. In the basic TSA, there are two different resolution mechanisms for balancing both local and global search technique. For this reason, basic TSA was preferred for parameter extraction of the PV module. The parameter results obtained by TSA were compared with those found by some other algorithms in the literature. According to the comparison result, the lowest root mean square error (RMSE) was obtained with the TSA algorithm. When the convergence graphs are examined, it is seen that TSA converges faster than other algorithms. When the box plots are analyzed, the results obtained by TSA have fewer outliers than the results of other algorithms, showing that TSA has a stable structure. In addition, a ranking graph was drawn according to the results obtained by all algorithms at each run time, and it was seen that TSA had the lowest RMSE value at all run times. Thus, it is concluded that TSA is a very competitive method for the PV module problem

A numerical study of the Burgers' equation

Time and space splitting techniques are applied to the Burgers' equation and the modified Burgers' equation, and then the quintic B-spline collocation procedure is employed to approximate the resulting systems. Some numerical examples are studied to demonstrate the accuracy and efficiency of the proposed method. Comparisons with both analytical solutions and some published numerical results are done in computational section. (C) 2007 The Franklin Institute. Published by Elsevier Ltd. All rights reserved

Quintic B-spline collocation method for numerical solution of the RLW equation

Quintic B-spline collocation schemes for numerical solution of the regularized long wave (RLW) equation have been proposed. The schemes are based on the Crank-Nicolson formulation for time integration and quintic B-spline functions for space integration. The quintic B-spline collocation method over finite intervals is also applied to the time-split RLW equation and space-split RLW equation. After stability analysis is applied to all the schemes, the results of the three algorithms are compared by studying the propagation of the solitary wave, interaction of two solitary waves and wave undulation

A B-spline algorithm for the numerical solution of Fisher's equation

Purpose - This paper seeks to develop an efficient B-spline Galerkin scheme for solving the Fisher's equation, which is a nonlinear reaction diffusion equation describing the relation between the diffusion and nonlinear multiplication of a species

Extended B-spline collocation method for KDV-Burgers equation

The extended form of the classical polynomial cubic B-spline function is used to set up a collocation method for some initial boundary value problems derived for the Korteweg-de Vries-Burgers equation. Having nonexistence of third order derivatives of the cubic B-splines forces us to reduce the order of the term uᵪᵪᵪ to give a coupled system of equations. The space discretization of this system is accomplished by the collocation method following the time discretization with Crank-Nicolson method. Two initial boundary value problems, one having analytical solution and the other is set up with a non analytical initial condition, have been simulated by the proposed method.Publisher's Versio

Three different methods for numerical solution of the EW equation

Numerical solutions of the equal width wave (EW) equation are obtained by using a Galerkin method with quartic B-spline finite elements, a differential quadrature method with cosine expansion basis and a meshless method with radial-basis functions. Solitary wave motion, interaction of two solitary waves and wave undulation are studied to validate the accuracy and efficiency of the proposed methods. Comparisons are made with analytical solutions and those of some earlier papers. The accuracy and efficiency are discussed by computing the numerical conserved laws and L-2, L-infinity error norms. (C) 2007 Elsevier Ltd. All rights reserved