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In this paper, one-dimensional heat equation subject to both Neumann and Dirichlet initial boundary conditions is presented and a spline Collocation Method is utilized for solving the problem. also Spline provides continuous solution in contrast to finite difference method, which only provides discrete approximations. It is found that this method is a powerful mathematical tool and can be applied to large class of linear and nonlinear problem in different fields of science and technology. Numerical results obtained by the present method are in a good agreement with the analytical solutions available in the literature.

One-Dimensional Heat Equation Subject to Both Neumann and Dirichlet Initial Boundary Conditions and Used a Spline Collocation Method