Variable-step variable-order algorithm for the numerical solution of neutral functional differential equations
A variable-step algorithm of variable order is developed for the numerical solution of neutral functional-differential equations of the form \[ y'(t)=f(t,y(\cdot),y'(\cdot),\quad t\in [a,b],\quad y(t)=g(t),\quad t\in [\gamma,a] \] where \(\gamma \leq a<b\). The algorithm is based on a predictor-corrector method with automatic control of step size and order. Although the error estimates are valid only under strong hypotheses, several numerical experiments indicate that the algorithm can be both accurate and efficient for neutral equations with variable delays under less stringent conditions. In the case of functional differential equations not of neutral type, further improvement of efficiency can be obtained by modifying the algorithm.
neutral functional-differential equations
scientific article; zbMATH DE number 4018271
scientific article