Abstract In this manuscript, we implement a spectral collocation method to find the solution of reaction–diffusion equation with some initial and boundary conditions. We approximate by using two-dimensional interpolating polynomial dependent Legendre–Gauss–Lobatto points. fully show that achieved solutions are convergent exact when number points increases. demonstrate capability efficiency prov...

A dynamic adaptive numerical method for solving partial differential equations on the sphere is developed. The method is based on second generation spherical wavelets on almost uniform nested spherical triangular grids, and is an extension of the adaptive wavelet collocation method to curved manifolds. Wavelet decomposition is used for grid adaption and interpolation. An OðN Þ hierarchical fini...

Non–intrusive Simplex Elements Stochastic Collocation, Stochastic Collocation with Clenshaw–Curtis points, and the Padé–Legendre method are applied to the transonic RAE 2822 airfoil test case of the NODESIM Workshop on Quantification of CFD Uncertainties. Uncertainty in a combination of the free stream Mach number M∞, angle of attack α, and thickness–to–chord ratio t/c described by uniform and ...

The paper presents a method to recover exponential accuracy at all points (including at the discontinuities themselves), from the knowledge of an approximation to the interpolation polynomial (or trigonometrical polynomial). We show that if we are given the collocation point values (or' an highly accurate approximation) at the Gauss or Gauss-Lobatto points, we can reconstruct an uniform exponen...