On some iterative numerical methods for a Volterra functional integral equation of the second kind
The paper is concerned with the numerical solution of a nonlinear Volterra integral equation of the form \[ x\left(t\right) = \lambda \int\limits_{-t}^{t} K\left(t,s,x\left(s\right)\right) d s + f\left(t\right), \quad t \in \left[-T,T\right], \] where the kernel \(K\) and the function \(f\) are continuous. The existence and uniqueness of the solution is proved under additional assumptions on the kernel. The author proposes a method that is based on the Picard's successive approximations and trapezoidal rule for computing integrals. The error estimates for the proposed method are derived and numerical experiments are presented to confirm the theoretical results.
scientific article; zbMATH DE number 6821149
scientific article