- This paper proposes a numerical method to solve for the moving boundary given by a beam of negligible mass on the surface of a thin film. The model leads to a sixth-order equation which is discretized in a way that readily represents the minimization of strain energy and conservation of mass. The discretized system is then coupled together and linearized via Newton's method. The Jacobian matrix is solved by using an appropriate algorithm, depending on the constraints and matrix structure.
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Numerical and asymptotic solution of a sixth-order nonlinear diffusion equation and related coupled systems
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