Spectral accuracy for solutions with twin boundary layers or several shocks

For problems whose solutions have several pairs of singularities close to the computational interval, usually characterised by fronts, shocks, and layers, an improvement on the exponential convergence rate of rational pseudospectral methods is presented. To define a new method, a conformal map is chosen to enlarge the ellipse of analyticity of the underlying solution. Numerical results demonstrate the accuracy and effectiveness of the proposed algorithm.