Unconditionally Stable and Convergent Difference Scheme for Superdiffusion with Extrapolation
Unconditionally Stable and Convergent Difference Scheme for Superdiffusion with Extrapolation
Abstract Approximating the Hadamard finite-part integral by the quadratic interpolation polynomials, we obtain a scheme for approximating the Riemann-Liouville fractional derivative of order $$\alpha \in (1, 2)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>∈</mml:mo> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> and the error is shown to have the asymptotic expansion $$ …