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    A Fully Implicit Finite Difference Approach for Numerical Solution of the Generalized Equal Width (GEW) Equation
    (Natl Acad Sciences India, 2020) Inan, Bilge; Bahadir, Ahmet Refik
    In this paper, a fully implicit finite difference method is presented to solve the generalized equal width equation. This implicit method allows to handle any values of p. Since the equation is nonlinear the scheme leads to a system of nonlinear equations. At each time step, Newton's method is used to solve this nonlinear system. The linear stability analysis of the proposed method is investigated using von Neumann approach and at the end of this investigation is seen that the method is unconditionally stable. The results are comparisons with analytical and other numerical values clearly show that results obtained using the fully implicit finite difference scheme are precise and reliable.
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    Numerical solution of the one-dimensional Burgers' equation: Implicit and fully implicit exponential finite difference methods
    (Indian Acad Sciences, 2013) Inan, Bilge; Bahadir, Ahmet Refik
    This paper describes two new techniques which give improved exponential finite difference solutions of Burgers' equation. These techniques are called implicit exponential finite difference method and fully implicit exponential finite difference method for solving Burgers' equation. As the Burgers' equation is nonlinear, the scheme leads to a system of nonlinear equations. At each time-step, Newton's method is used to solve this nonlinear system. The results are compared with exact values and it is clearly shown that results obtained using both the methods are precise and reliable.
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    Numerical Solutions of MRLW Equation by a Fully Implicit Finite-Difference Scheme
    (Journal Mathematics & Computer Science-Jmcs, 2015) Inan, Bilge; Bahadir, Ahmet Refik
    In the present paper, a fully implicit finite difference method is introduced for the numerical solution of the modified regularized long wave (MRLW) equation. The accuracy of the method is examined by different problems of the MRLW equation. The results and comparisons with analytical and other numerical invariants clearly show that results obtained using the fully implicit finite difference scheme are precise and reliable.