A collocation method for the solution of nonlinear one-dimensional parabolic equations
نویسندگان
چکیده
In this paper, we develop a collocation method based on cubic B-spline to the solution of nonlinear parabolic equation εuxx = a(x, t)ut + φ(x, t, u, ux) subject to appropriate initial, and Dirichlet boundary conditions, where ε > 0 is a small constant. We developed a new two-level three-point scheme of order O(k + h). The convergence analysis of the method is proved. Numerical results are given to illustrate the efficiency of our method computationally.
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