Portal de Periódicos da CAPES

Differentiating matrices for arbitrarily spaced grid points

1986; Wiley; Volume: 23; Issue: 2 Linguagem: Inglês

10.1002/nme.1620230205

1097-0207

W. D. Lakin,

Electromagnetic Simulation and Numerical Methods

Abstract Differentiating matrices allow the numerical differentiation of functions defined at points of a discrete grid. Previous derivations of these matrices have been restricted to grids with uniformly spaced points, and the resulting derivative approximations have lacked precision, especially at endpoints. The present work derives differentiating matrices on grids with arbitrarily spaced points. It is shown that high accuracy can be achieved through use of differentiating matrices on non‐uniform grids through the expedient of including ‘near‐ boundary’ points. Use of the differentiating matrix as an operator in the solution of problems involving ordinary differential equations is also considered.