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In this paper, efficient numerical schemes are proposed for solving the fractional water wave models that describe the propagation of surface water wave. By using the weighted and shifted Grünwald–Letnikov (WSGL) formula to approximate the nonlocal fractional operators, we design a series of second order accurate difference schemes for the considered models. The existence, stability and convergence of numerical solutions of the proposed numerical schemes are established rigorously. The analysis shows that the proposed numerical schemes are unconditionally stable with second order accuracy for both temporal and spatial discretizations. Several numerical results are provided to verify the efficiency and accuracy of our theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, we develop a numerical approximation to the solution of a system of integral equations arising from a nonlocal hyperbolic reliability model. Convergence of this numerical method is proved. And this numerical scheme is used to study the behavior of the solution. [Copyright &y& Elsevier]