For the time fractional sub-diffusion equation with variable coefficients, a quintic spline method is presented, along the time direction, the recursion formula obtained from the Lagrange interpolation functions is used, along the space direction, the quintic spline interpolation functions, which have high order accuracy when being used to approximate smooth functions and their 1,2,3 order derivatives, are used as the basis functions. Theoretical analyses and numerical examples show that 4 order accuracy in space can be achieved for this scheme.
Sub-diffusion equation, quintic spline collocation method, fractional
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