When is Runge-Kutta not applicable?

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In time stepping, there's BDF, generalized alpha and Runge-Kutta. When is Runge-Kutta not applicable, showing an error message?


4 Replies Last Post Mar 27, 2025, 7:01 a.m. EDT
Robert Koslover Certified Consultant

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Posted: 1 week ago Mar 23, 2025, 11:31 a.m. EDT
Updated: 1 week ago Mar 23, 2025, 11:32 a.m. EDT

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 **

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Scientific Applications & Research Associates (SARA) Inc.
www.comsol.com/partners-consultants/certified-consultants/sara
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 **

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Posted: 6 days ago Mar 26, 2025, 3:22 a.m. EDT
Updated: 5 days ago Mar 26, 2025, 10:37 a.m. EDT

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

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

Robert Koslover Certified Consultant

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Posted: 5 days ago Mar 26, 2025, 9:30 p.m. EDT
Updated: 5 days ago Mar 26, 2025, 9:36 p.m. EDT

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."

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Scientific Applications & Research Associates (SARA) Inc.
www.comsol.com/partners-consultants/certified-consultants/sara
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."

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Posted: 4 days ago Mar 27, 2025, 7:01 a.m. EDT
Updated: 3 days ago Mar 28, 2025, 10:09 a.m. EDT

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.
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.

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