Numerical solution methods for distributed order differential equations. (English) Zbl 1032.65070
Summary: We introduce a basic framework for the numerical solution of distributed order differential equations. Equations of this type have appeared in several recent papers and the need for reliable numerical methods for their solution is apparent. We consider how distributed order equations may be solved through the use of an approximating multi-term equation. We use our recent methods for this problem to yield an approximate solution. We illustrate our approach using a simple example distributed order equation and give numerical evidence that indicates the convergence of our method.
MSC:
65L05 | Numerical methods for initial value problems involving ordinary differential equations |
45J05 | Integro-ordinary differential equations |
65R20 | Numerical methods for integral equations |
34A34 | Nonlinear ordinary differential equations and systems |
26A33 | Fractional derivatives and integrals |
65L20 | Stability and convergence of numerical methods for ordinary differential equations |