| dc.description | In this thesis, an orthogonal spline collocation algorithm is formulated and implemented within a method-of-lines approach for the numerical solution of a class of linear parabolic partial differential equations. A detailed implementation of the orthogonal spline collocation algorithm for solving elliptic partial differential equations (PDEs) is given and the efficiency of the implementation is discussed. By collocating the elliptic PDEs at Gaussian points, a linear system in tensor product form is obtained. A matrix decomposition approach is used to reduce the linear system to a collection of independent almost block diagonal linear systems, each of which is solved by the almost block diagonal linear system solver ARCECO. The same approach is then applied within a method-of-lines context to solve partial differential equations of parabolic type. By collocating the parabolic PDE at Gaussian points, systems of ordinary differential equations (ODES) are generated. The Jacobian matrix of the ODE system has an almost block diagonal structure. This ODE system is solved using the differential/algebraic solver DASSL, which is modified to take advantage of the special structure of the Jacobian matrix. These algorithms are efficiently implemented in a parallel architecture, using an eight processor Alliant/FX2800. Numerical experiments are presented to demonstrate the parallel performance of these algorithms. | en_US |
