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I'm not sure abut that, but the info at this link may help you decide which method to use: **https://www.comsol.com/support/knowledgebase/1062 **

Dr Koslover, Thank you. There is just one sentence about Runge-Kutta, which says it is not as efficient for PDEs without further explanation.

I don't know the specific conditions Comsol uses to generate an error message, but you might be able to find out by asking Comsol Support directly. Meanwhile, in regard to the title of your post, "When is Runge-Kutta not applicable," I found that if you copy that question into Google search, you'll get a rather nice AI-generated explanation and summary. In fact, there is quite a lot of information available on the internet concerning the applicability, or not, of Runge-Kutta methods in regard to various kinds of problems.

Also, according to another Comsol Knowledgebase item at: https://www.comsol.com/support/knowledgebase/1262 , "the Runge-Kutta methods are used primarily for solving systems of ODEs and for models involving the Time Explicit Pressure Acoustics and Time Explicit Electromagnetic Waves physics interfaces. As such, they are quite narrow in their usage, and are not covered within the scope of this Knowledgebase Article."

Dr Koslover, Thank you. The Info you provided is very helpful.

A usual error message when applying Runge-Kutta to PDEs is (even when the mass matrix is taken as a constant!):

• Feature: Time-Dependent Solver 1 (sol1/t1) Mass matrix may depend on solution or time. Reformulate the equation or use an implicit solver.