We propose a Legendre-Petrov-Galerkin Chebyshev spectral collocation method for initial value problems (IVPs) of second-order nonlinear ordinary differential equations (ODEs). The is applied to time discretization and the term dealt with method. scheme results in simple algebraic system by choosing appropriate basis functions. Optimal error estimates $ L^2 $-norm single multiple interval method...

For many boundary element methods applied to Laplace's equation in two dimensions, the resulting integral equation has both an integral with a logarithmic kernel and an integral with a discontinuous kernel. If standard collocation methods are used to discretize the integral equation we are left with two dense matrices. We consider expressing these matrices in terms of wavelet bases with compact...