Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solvability of boundary value problems for systems of singular differential-algebraic equations
SIAM Journal on Mathematical Analysis
Implicit Runge-Kutta methods for some integrodifferential-algebraic equations
Selected papers of the sixth conference on Numerical Treatment of Differential Equations
Multilinear Volterra Equations of the First Kind
Automation and Remote Control
Development of the normal spline method for linear integro-differential equations
ICCS'03 Proceedings of the 2003 international conference on Computational science: PartII
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Systems of integral-differential equations with a singular matrix multiplying the highest derivative of the unknown vector function are considered. An existence theorem is formulated, and a numerical solution method is proposed. The solutions to singular systems of integral-differential equations are unstable with respect to small perturbations in the initial data. The influence of initial perturbations on the behavior of numerical processes is analyzed. It is shown that the finite-difference schemes proposed for the systems under study are self-regularizing.