Abstract:
Nodal integral methods (nim) are numerical methods which solves partial differential equations in quite efficient and accurate manner. The available conventional methods such as finite difference method (fdm) or finite volume methods (fvm) need very fine mesh compared to nim to attain the same level of accuracy. The high accuracy of nim is due to the use of semi analytic solutions of approximate odes for each node in the mesh. In spite of significant merits over other methods, the prevailing use of nim is limited only for linear or weakly nonlinear problems. Recently, some efforts have been made to extend the application of nim for higher non-linearity by using jacobian-free newton krylov (jfnk) approach which is an efficient implementation of the newton method. A preconditioning algorithm of jfnk is given for burger’s equation in both dimension in 1d and 2d, but the work was not extended for higher nonlinearity because of the singularities in the coefficients at higher reynolds numbers. In the present study, some modifications in the coefficients are given to extend the algorithm for relatively high nonlinearity compared to earlier work. The numerical results are compared with the analytical solution to demonstrate the accuracy of the proposed algorithm. Furt hermore, the spectral analysis is performed to test the eigenvalues clustering ability of the proposed algorithm. © 2022, avestia publishing. All rights reserved.