Numerical solution of neutral functional differential equations by Adams methods in divided difference form
An algorithm of variable step and variable order for the numerical solution of neutral functional differential equations (NFDE) is described. The form of NFDE are: \[ \begin{aligned} y'(t) &= f\bigl(t,y(\bullet),y'(\bullet)\bigr), \;t\in[a,b]\\ y(t)& =g(t),\;t\in[\tau,\alpha],\;y'(t)=g'(t),\;t\in[\tau,\alpha] \end{aligned} \] with \(\tau\leq\alpha<b\) and \(g\in C_n^1[\tau,\alpha]\) is a given initial function. The algorithm for the solution of the above system is based on the variable step formulation of the Adams methods represented in divided difference form in which the Adams-Bashforth and Adams-Moulton methods are implemented in predictor-corrector mode. The restarting of the integration at each discontinuity point (derivative discontinuities) relies on the step size and order changing strategy based on the estimates of the local discretization errors. The algorithm reduces the computational cost and increases the reliability and efficiency by obtaining asymptotically correct estimates of the local discretization errors. The method is tested in three test examples.
neutral functional differential equations
scientific article; zbMATH DE number 5015155