Collocation methods for solving multivariable integral equations of the second kind (Q442743)

The authors construct a method to approximate solving the integral equation of second kind NEWLINE\[NEWLINE \lambda \rho(x)-\int_{R} a(x,y) \rho(y)dy =\psi(x), \qquad x \in{R}, NEWLINE\]NEWLINE where \(R\) is a closed polygonal region in \(\mathbb R^{2}\). This method is based on an interpolatory projection onto a space of piecewise polynomials that are constructed using the triangulation of the domain \(R\). In fact this construction represents a particular case of the known collocation method.