On Numerical Algorithms for the Solution of a Beltrami Equation

The paper concerns numerical algorithms for solving the Beltrami equation $f_{\bar{z}}(z)=\mu (z)f_z(z)$ for a compactly supported $\mu$. First, we study an efficient algorithm that has been proposed in the literature, and present its rigorous justification. We then propose a different scheme for solving the Beltrami equation which has a comparable speed and accuracy, but has the virtue of a greater simplicity of implementation.