If euler explicit is used for the time derivative and, Mechanical Engineering

If euler explicit is used for the time derivative and

Though the PDEs

are identical analytically, they differ when finite-differenced. If Euler explicit is used for the time derivative, and first-order backward differencing is used for the spatial derivative, which FDE will maintain the conservative property?

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Mechanical Engineering: If euler explicit is used for the time derivative and

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Mechanical Engineering: If euler explicit is used for the time derivative and

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