On the convergence of difference schemes for differential equations with a fractional derivative. (English. Russian original) Zbl 0895.65037
Dokl. Math. 53, No. 3, 426-428 (1996); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 348, No. 6, 746-748 (1996).
The author gives some statements on convergence of Samarskij’s type difference schemes for the boundary value problem
\[
\frac{d}{dx} \left[k(x)\frac{du}{dx}\right] -r(x)D_{0x}^\alpha u - q(x)u= -f(x), \quad u(0)=u(1)=0,
\]
where \(k(x)\geq c_0>0, r(x)\geq 0\), \(q(x)\geq 0\) and \(D_{0x}^\alpha u\) is the Riemann-Liouville fractional derivative, \(0< \alpha <1\).
Reviewer: S.G.Samko (Faro)
MSC:
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
| 26A33 | Fractional derivatives and integrals |
| 65L12 | Finite difference and finite volume methods for ordinary differential equations |
| 34B05 | Linear boundary value problems for ordinary differential equations |
