Sinc galerkin-collocation for parabolic equation



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In this thesis we develop the Sinc-Galerkin collocation method for approximating the solution of initial boundary value problems for the heat equation in a finite space-time cylinder. One important feature of the Sine method is that a uniform exponential error bound is obtained, for boundary data in an appropriate class of functions. Further, the results are obtained in a finite time interval. The case of a finite time interval requires additional care in evaluating the resulting inner products to obtain well-conditioned matrices for the numerical solution of the resulting system of equations . This result appears to be a new result and allows for the solution of problems with boundary data which could not be used for an infinite time interval. When the weights and nodes are taken to be the same in each space variable, the resulting system of equations can be written in a particularly simple form involving tenser products. Using an eigenvalue decomposition method, the system can be very accurately solved using parallel computation.



Heat equation -- Numerical solutions, Finite element method -- Data processing, Eigenfunctions, Differential equations, Parabolic