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Test case, travelling wave on a string

The purpose of this test case is to verify that the simulation model is second order accurate for the time integration applied on a wave travelling on a string (balance between inertia and line forces). A travelling wave has been computed numerically and comparisons are made with the analytically calculated exact solution. The calculations were done for a string with controlled/fixed vertical position at the left boundary and the right boundary free to move vertically.

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The kinetic energy and work at boundary for the travelling wave

The relative error norm versus no of spatial grid divisions is presented below verifying second order error decay.