Special versions of the collocation method for integro-differential equations in the singular case
The paper discusses two numerical methods for solving the linear singular Fredholm integro-differential equation \(x(t) \prod_{j=1}^q (t - t_j)^{m_j} + \sum_{j=0}^p \int_{-1}^1 K_j(t,s) x^{(j)}(s) ds = y(t)\). The methods are of collocation type. The first method is based on Bernstein operators, the second one employs Hermite-Fejér interpolation techniques. An error analysis is provided in both cases.
linear singular Fredholm integro-differential equation
scientific article; zbMATH DE number 6819864