Spline approximations of solution of singular integro-differential equation. (English. Russian original) Zbl 1029.65148
Russ. Math. 45, No. 11, 32-43 (2001); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2001, No. 11, 35-45 (2001).
Introduction: For the equation
\[
\varphi'(t)+ a(t)\varphi(t)+{b(t)\over \pi} \int^1_{-1} {\varphi(t)d\tau\over\tau- t}= f(t),\quad -1\leq t\leq 1,
\]
with initial condition \(\varphi(-1)= 0\) computational schemes of the spline-collocation and spline-subdomain methods are given together with a theoretical substantiation of the methods.
MSC:
| 65R20 | Numerical methods for integral equations |
| 45E05 | Integral equations with kernels of Cauchy type |
| 45J05 | Integro-ordinary differential equations |
