We consider the stiffness matrices coming from the Galerkin B-spline isogeometric analysis approximation of classical elliptic problems. By exploiting specific spectral properties compactly described by a symbol, we design efficient multigrid methods for the fast solution of the related linear systems. We prove the optimality of the two-grid methods (in the sense that their convergence rate is ...

Nonnegative bivariate interpolants to scattered data are constructed using some C macro-element spline spaces. The methods are local, and rely on adjusting gradients at the data points to insure nonnegativity of the spline when the original data is nonnegative. More general range-restricted interpolation is also considered.

in this work, we proposed an efective method based on cubic and pantic b-spline scaling functions to solve partial differential equations of frac- tional order. our method is based on dual functions of b-spline scaling func- tions. we derived the operational matrix of fractional integration of cubic and pantic b-spline scaling functions and used them to transform the mentioned equations to a ...

We use trivariate spline functions for the numerical solution of Dirichlet problem 3D elliptic Monge-Ampére equation. Mainly we collocation method introduced in [SIAM J. Numerical Analysis, 2405-2434,2022] to numerically solve iterative Poisson equations and an averaged algorithm ensure convergence iterations. shall also establish rate under a sufficient condition provide some evidence show rat...

The application of collocation methods using spline basis functions to solve differential model equations has been in use for a few decades. However, the application of spline collocation to the solution of the nonlinear, coupled, partial differential equations (in primitive variables) that define the motion of fluids has only recently received much attention. The issues that affect the effecti...