Spline collocation-interpolation method for linear and nonlinear cordial Volterra integral equations. (English) Zbl 1215.65205
The author investigates the applicability and convergence of spline collocation and collocation-interpolation methods for linear and nonlinear cordial Volterra integral equations of the second kind with noncompact operators
\[ \begin{alignedat}{2}2 \mu u(t) &= \int^{t}_{0}t^{-1}\varphi(t^{-1} s)a(t,s)u(s) ds + f(t), \quad&&0 \leq t \leq T, \\ \mu u(t) &= \int^{t}_{0}t^{-1}\varphi(t^{-1} s)g(t,s,u(u)) ds + f(t), \quad&&0 \leq t \leq T. \end{alignedat} \]
The convergence speed of the considered methods is given, too.
\[ \begin{alignedat}{2}2 \mu u(t) &= \int^{t}_{0}t^{-1}\varphi(t^{-1} s)a(t,s)u(s) ds + f(t), \quad&&0 \leq t \leq T, \\ \mu u(t) &= \int^{t}_{0}t^{-1}\varphi(t^{-1} s)g(t,s,u(u)) ds + f(t), \quad&&0 \leq t \leq T. \end{alignedat} \]
The convergence speed of the considered methods is given, too.
Reviewer: I. V. Boikov (Penza)
MSC:
| 65R20 | Numerical methods for integral equations |
| 45A05 | Linear integral equations |
| 45D05 | Volterra integral equations |
| 45G10 | Other nonlinear integral equations |
Keywords:
cordial Volterra operators; non compact operators; nonlinear operators; spline collocation; Volterra integral equations; convergence; collocation-interpolation methodsReferences:
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