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The motion of the thin structure is governed by a generalized Euler Bernoulli beam model, and these equations are solved in a Lagrangian frame using two approaches, one based on finite differences and the other on finite elements.
The order of the influence matrix is twice larger than one would expect from analogous solution methods based on finite differences or finite elements.
The coupled system is solved by using a simple numerical scheme based on finite differences.
The quasilinearization method based on finite differences was used by Ramos [26] for solving the GRLW equation.
The most widely used methods for the solution of boundary value problems are based on finite differences.
Hence, it has generally been avoided when bending systems are considered; instead, approaches based on finite differences have been used.
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The first one which is based on finite difference model calculates the welding width and its penetration by utilizing heat transfer equations.
Moghaddam and Tenreiro Machado [22 24] proposed algorithms based on finite difference approximations and B-spline interpolation for different definitions of V-OF derivatives.
The algorithm is based on finite difference explicit implicit method.
The q-calculus theory is a novel theory that is based on finite difference re-scaling.
The method, which is very easy to implement, is based on finite difference discretization.
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