Numerical methods for stochastic Volterra integral equations with weakly singular kernels

COLLOCATION METHOD FOR FREDHOLM-VOLTERRA INTEGRAL EQUATIONS WITH WEAKLY KERNELS

In this paper it is shown that the use of‎ ‎uniform meshes leads to optimal convergence rates provided that‎ ‎the analytical solutions of a particular class of‎ ‎Fredholm-Volterra integral equations (FVIEs) are smooth‎.

collocation method for fredholm-volterra integral equations with weakly kernels

in this paper it is shown that the use of‎ ‎uniform meshes leads to optimal convergence rates provided that‎ ‎the analytical solutions of a particular class of‎ ‎fredholm-volterra integral equations (fvies) are smooth‎.

The semi-explicit Volterra integral algebraic equations with weakly singular kernels: The numerical treatments

A Hybrid Collocation Method for Volterra Integral Equations with Weakly Singular Kernels

The commonly used graded piecewise polynomial collocation method for weakly singular Volterra integral equations may cause serious round-off error problems due to its use of extremely nonuniform partitions and the sensitivity of such time-dependent equations to round-off errors. The singularity preserving (nonpolynomial) collocation method is known to have only local convergence. To overcome th...

Product integration for Volterra integral equations of the second kind with weakly singular kernels

We introduce a new numerical approach for solving Volterra integral equations of the second kind when the kernel contains a mild singularity. We give a convergence result. We also present numerical examples which show the performance and efficiency of our method.