Numerical solution of linear Volterra equations with partial integrals
The author generalizes the application of the Gauss quadrature method to approximately solve the second kind Volterra integral equation \[ x(t,s)=(Kx)(t,s)+ f(t,s), \] defined on the space \( C(D)\), \(D= [a,b]\times [c,d]\) of functions of two variables. The theorem proves the convergence of the quadrature method, imposing several conditions on the step size, the coefficients of the formula and others. The class of quadrature formulas that correspond to these assumptions is not specified.
scientific article; zbMATH DE number 6534005