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Development of Structure-preserving Numerical Methods for Partial Differential Equations

Numerical methods that inherit some mathematical structures or properties from the original differential equations are called "structure-preserving numerical methods" in general.

There exist various studies about structure-preserving methods for ordinary differential equations, which include some famous studies about symplectic methods. In the context for partial differential equations, however, we have no framework study until our study of "discrete variational derivative method" which treats conservative or dissipative partial differential equations in the end of 1990s.

So far, we have developed the method with many colleagues.

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