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With standard numerical methods on uniform grids, very small mesh parameters and very small timesteps must be used to correctly resolve the fine details of the sharp and rapidly changing wave fronts.
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Numerical results show the good performance of the method on uniform, skewed as well as composite meshes and confirm convergence at optimal rates.
Numerical tests are carried out to support the theoretical results and comparing with the method on uniform grid shows the efficiency of our methods.
In actual computation, the Q2-Q1 mixed finite element method on uniform grid is used to generate discretizations.
Furthermore, we observed that Phuengrattana [14] studied approximating fixed points of for a nonlinear mapping T with condition (C) by the Ishikawa iteration method on uniform convex Banach space with Opial property.
To name a few, Mohanty et al. [11 13] developed AGE, cubic spline TAGE, Newton-TAGE iteration methods using a finite difference and cubic spline method based on uniform and non-uniform mesh, respectively, to solve non-linear singular two point boundary value problems.
Higher-order finite difference methods on a uniform mesh for the solution of nonlinear parabolic equations were proposed by Jain et al. [10].
An optimization method based on uniform design in conjunction with genetic algorithm is described.
An efficient numerical method based on uniform Haar wavelets is proposed for the numerical solution of second-order boundary-value problems (BVPs) arising in the mathematical modeling of deformation of beams and plate deflection theory, deflection of a cantilever beam under a concentrated load, obstacle problems and many other engineering applications.
Comparison of MLS, GPQ and Bayes method performance on uniform and gamma data.
We present de-aliasing rules to be used when evaluating non-linear terms with polynomial spectral methods on non-uniform grids analogous to the de-aliasing rules used in Fourier spectral methods.
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