$$\boldsymbol{\mathbb{R}}$$-Linear Problem for a Circular Domain and Its Application to Composites

We develop the method of functional equations to solve the $$\mathbb{R}$$ -linear problem for analytic functions for a circular coated domain. The solution is obtained in the form of series in symbolic form. Numerical examples are given, and the accuracy of the obtained solutions are analyzed. The $$\mathbb{R}$$ -linear problem models antiplane shear in elastic fiber composites.