Sinc methods for quadrature and differential equations
Sinc methods for quadrature and differential equations
Numerical solution of the heat equation with nonlocal boundary conditions
Journal of Computational and Applied Mathematics
Stability in the numerical solution of the heat equation with nonlocal boundary conditions
Applied Numerical Mathematics
Efficient techniques for the second-order parabolic equation subject to nonlocal specifications
Applied Numerical Mathematics
Application of Sinc-collocation method for solving an inverse problem
Journal of Computational and Applied Mathematics
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In this paper, the problem of solving the parabolic partial differential equations subject to given initial and nonlocal boundary conditions is considered. We change the problem to a system of Volterra integral equations of convolution type. By using Sinc-collocation method, the resulting integral equations are replaced by a system of linear algebraic equations. The convergence analysis is included, and it is shown that the error in the approximate solution is bounded in the infinity norm by the condition number of the coefficient matrix multiplied by a factor that decays exponentially with the size of the system. Some examples are considered to illustrate the ability of this method.