Applied Mathematics and Computation
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
A perspective on the numerical treatment of Volterra equations
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Sensitivity analysis for dynamic systems with time-lags
Journal of Computational and Applied Mathematics
Identification of the initial function for discretized delay differential equations
Journal of Computational and Applied Mathematics
Applied Numerical Mathematics
Discontinuous solutions of neutral delay differential equations
Applied Numerical Mathematics
Identification of the initial function for discretized delay differential equations
Journal of Computational and Applied Mathematics
Some aspects of causal & neutral equations used in modelling
Journal of Computational and Applied Mathematics
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It is known that Alekseev's variation of parameters formula for ordinary differential equations can be generalized to other types of causal equations (including delay differential equations and Volterra integral equations), and corresponding discrete forms. Such variation of parameters formulae can be employed, together with appropriate inequalities, in discussing the behaviour of solutions of continuous and discretized problems, the significance of parameters in mathematical models, sensitivity and stability issues, bifurcation, and (in classical numerical analysis) error control, convergence and super-convergence of densely defined approximations and error analysis in general. However, attempts to extend Alekseev's formula to nonlinear Volterra integral equations are not straightforward, and difficulties can recur in attempts to analyze the sensitivity of functionally-dependent or structurally-dependent solutions.In analyzing sensitivity we discuss behaviour for infinitesimally small perturbations. In discussions of stability we need to establish the existence of bounds on changes to solutions (or their decay in the limit as t → ∞) that ensue from perturbations in the problem. Yet the two topics are related, not least through variation of parameters formulae, and (motivated by some of our recent results) we discuss this and related issues within a general framework.