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A numerical method is developed for solving parabolic partial differential equations with integral boundary conditions. The method is moderately sixth-order accurate due to merging of sixth order finite difference scheme and fifth order Pade's approximation. Simpson's 1/3 rule is used to approximate integral conditions. The method does not involve the use of complex arithmetic and optimizes the results. It is observed that this numerical method can be easily coded on serial as well as parallel computers.

Hybrid Numerical Method for Heat Equation with Nonlocal Boundary Conditions in Parallel Computing Environment