This paper analyzes the stability and convergence of the Fourier pseudospectral method coupled with a variety of specially designed time-stepping methods of up to fourth order, for the numerical solution of a three dimensional viscous Burgers’ equation. There are three main features to this work. The first is a lemma which provides for an L2 and H 1 bound on a nonlinear term of polynomial type,...

Consider the linear system Ax=b where the coefficient matrix A is an M-matrix. In the present work, it is proved that the rate of convergence of the Gauss-Seidel method is faster than the mixed-type splitting and AOR (SOR) iterative methods for solving M-matrix linear systems. Furthermore, we improve the rate of convergence of the mixed-type splitting iterative method by applying a preconditio...

The modelling of financial markets as continuous stochastic processes provides the means to analyse the implications of models and to compute prices for a host of financial instruments. We code as a symbolic computing program the analysis, initiated by Black, Scholes and Merton, of the formation of a partial differential equation whose solution is the value of a derivative security, from the sp...

We present a new reduced scaling multireference singles and doubles configuration interaction ~MRSDCI! algorithm based upon the combination of local correlation and pseudospectral methods. Taking advantage of the locality of the Coulomb potential, the weak-pairs approximation of Saebo” and Pulay is employed to eliminate configurations having simultaneous excitations out of pairs of distant, wea...

The smoothness-constrained least-squares method is widely used for two-dimensional (2D) and three-dimensional (3D) inversion of apparent resistivity data sets. The Gauss–Newton method that recalculates the Jacobian matrix of partial derivatives for all iterations is commonly used to solve the least-squares equation. The quasi-Newton method has also been used to reduce the computer time. In this...