Novel rational spectral collocation is presented in combination with singularity separation method for the second-order singularly perturbed boundary-value problems. The solution form u = w + υ; where of corresponding third problem and υ a singular function explicit expression. auxiliary solved by combined asymptotic theory (RSCAT). According to analysis, parameters sinh-transformation can be d...

In this paper, we present the multilevel adaptive wavelet collocation method for solving non-divergent barotropic vorticity equation over spherical geodesic grid. This method is based on multi-dimensional second generation wavelet over a spherical geodesic grid. The method is more useful in capturing, identifying, and analyzing local structure [1] than any other traditional methods (i.e. finite...

In this paper, we consider the Legendre spectral Galerkin and Legendre spectral collocation methods to approximate the solution of Urysohn integral equation. We prove that the approximated solutions of the Legendre Galerkin and Legendre collocation methods converge to the exact solution with the same orders, O(n−r) in L2-norm and O(n 1 2 −r) in infinity norm, and the iterated Legendre Galerkin ...

In this paper, we present a numerical scheme based on collocation method to solve stochastic non-linear Poisson–Boltzmann equations (PBE). This equation is generalized version of the arising from form biomolecular modeling case. Applying radial basis functions (RBFs) allows us deal with difficulties complexity domain. To indicate accuracy RBF method, results for two-dimensional models, also stu...