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

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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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