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Abstract
An approximate method for solving the diffusion equation with nonlocal boundary conditions is proposed. The method is based upon constructing the double shifted Legendre series to approximate the required solution using Legendre tau method. The differential and integral expressions which arise in the diffusion equation with nonlocal boundary conditions are converted into a system of linear algebraic equations which can be solved for the unknown coefficients. Numerical examples are included to demonstrate the validity and applicability of the method and a comparison is made with existing results.