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In a previous paper, a technique was suggested to avoid order reduction withany explicit exponential Runge-Kutta method when integrating initial boundaryvalue nonlinear problems with time-dependent boundary conditions. In thispaper, we significantly simplify the full discretization formulas to be appliedunder conditions which are nearly always satisfied in practice. Not only asimpler linear combination of $\varphi_j$-functions is given for both thestages and the solution, but also the information required on the boundary isso much simplified that, in order to get local order three, it is no longernecessary to resort to numerical differentiation in space. The technique isthen shown to be computationally competitive against other widely used methodswith high enough stiff order through the standard method of lines.

Simplified explicit exponential Runge-Kutta methods without order reduction