Collocation and iterated collocation methods for a class of weakly singular Volterra integral equations

By Teresa Diogo. 2009

53 citations recorded by the source corpus.

We discuss the convergence properties of spline collocation and iterated collocation methods for a weakly singular Volterra integral equation associated with certain heat conduction problems. This work completes the previous studies of numerical methods for this type of equations with noncompact kernel. In particular, a global convergence result is obtained and it is shown that discrete superconvergence can be achieved with the iterated collocation if the exact solution belongs to some appropriate spaces. Some numerical examples illustrate the theoretical results.

Subfields: Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/1c3c43302f5916dc0bd7ea5fb94ecb62b737e947

Citations in the corpus

• Solution of Nonlinear Volterra Integral Equations with Weakly Singular Kernel by Using the HOBW Method (2019, unknown): “Numerical strategies for the SNVIE are spline collocation methods [3], Newton–Cotes methods [4], extrapolation algorithm [5], and Hermite-collocation method [6].”