Hermite interpolant multiscaling functions for numerical solution of the convection diffusion equations

Abstract

A numerical technique based on the Hermite interpolant multiscaling functions is presented for the solution of Convection-diffusion equations. The operational matrices of derivative, integration and product are presented for multiscaling functions and are utilized to reduce the solution of linear Convection-diffusion equation to the solution of algebraic equations. Because of sparsity of these matrices, this method is computationally very attractive and reduces the CPU time and computer memory. Illustrative examples are included to demonstrate the validity and applicability of the new technique.Key Words: Hermite interpolant multiscaling functions, Convection-diffusion equation, operational matrix of derivative, Operational matrix of integration, operational matrix of product.

Modified Variational Iteration Algorithm-II: Convergence and Applications to Diffusion Models

“…e numerical results of the MVIA-II for Test Problem 4.3 are reported in Table 4 along with the exact solution and the results in the recent literature. It can be noticed from the table that the MVIA-II gives more accurate results in comparison with the approaches given in [15,48]. e accuracy of the suggested MVIA-II is also verified from Figure 4, whereas in Figure 5, we have shown the absolute error for various time instants t � 0.3, t � 0.5, and t � 1.0.…”

“…In Table 3, we compare the results generated by the MVIA-II with the exact one and with the method reported in [48] for Test Problem 4.2. From this table, we can conclude that the proposed algorithm produces better results than the results of a technique based on Hermite interpolant multiscaling functions given in [48].…”

“…e absolute error for times t � 0.3, t � 0.6, and t � 0.9 is shown in Figure 3, and superb accuracy has been archived in this case as well. [48] of the following form:…”