The author solves numerically a Beltrami differential equation of type \[ (*)\quad (\partial /\partial \bar z)f(z)=\mu (z)(\partial /\partial z)f(z). \] This is a differential equation in the complex plane, where \(\mu\) is a given complex function required to satisfy \(\| \mu \|_{\infty}<1\) which implies quasiregularity of the wanted functions f. The numerical solution of (*) is achieved by applying complex planar splines. These splines are in spirit finite elements with complex coefficients. The advantage of using these splines is that one does not need to split the differential equation into real and imaginary part. The author studies the so-called Goursat problem on a triangle where certain boundary conditions have to be fulfilled. He uses a triangular mesh and proposes an algorithm for which he proves linear convergence in uniform norm in dependence of the meshsize of the triangular grid. There are two numerical examples which mirror the theory well. In addition there is a section on improving on the convergence rate by applying extrapolation techniques repeatedly. This technique is also illustrated by an example.