一类Riesz空间分数阶对流弥散方程的差分方法

Difference methods for a class of Riesz space fractional convection dispersion equations

对带有分数阶边界条件的一类Riesz空间分数阶方程,提出了求解该方程的隐式差分格式,得到了离散后的矩阵格式.理论分析了隐式差分格式解满足存在唯一性、具有无条件稳定以及依无穷范数收敛的特性.所给数值算例验证了隐式差分方法的可行性.

For a class of Riesz space fractional order equation with fractional boundary condition, an implicit difference scheme of the equation is proposed, and the discrete matrix scheme is worked out. Moreover, theoretical analysis is conducted to prove the solution to the implicit difference scheme is unique in terms of existence, unconditional in terms of stability and with convergence of solutions in infinite norm. The obtained results of numerical examples proved the feasibility of the implicit difference scheme.