Numerical methods for differential equations

An asymptotic iteration method for solving second-order homogeneous linear differential equations of the form y ″ = λ 0 ( x ) y ′ + s 0 ( x ) y is introduced, where λ 0 ( x ) ≠ 0 and s 0 ( x ) are C ∞ functions. Applications to Schrödinger-type problems, including some with highly singular potentials, are presented.

• HAKAN ÇİFTCİ

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• FATMA AYAZ

In this paper, it is shown that the problem of checking the solvability of a bilinear matrix inequality (BMI), is NP-hard. A matrix valued function, F(X,Y), is called bilinear if it is linear with respect to each of its arguments, and an inequality of the form, F(X,Y)>0 is called a bilinear matrix inequality. Recently…

Article The Use of Variational Iteration Method, Differential Transform Method and Adomian Decomposition Method for Solving Different Types of Nonlinear Partial Differential Equations was published on March 1, 2006 in the journal International Journal of Nonlinear Sciences and Numerical Simulation (volume 7, issue 1).

The present monograph is devoted to the construction and investigation of the new high order of accuracy difference schemes of approximating the solutions of regular and singular perturbation boundary

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• FATMA AYAZ

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The book is mainly about hybrid systems with continuous/discrete-time dynamics. The major part of the book consists of the theory of equations with piece-wise constant argument of generalized type. The systems as well as technique of investigation were introduced by the author very recently. They both generalized know…

The exp-function method is presented for finding the exact solutions of nonlinear fractional equations. New solutions are constructed in fractional complex transform to convert fractional differential equations into ordinary differential equations. The fractional derivatives are described in Jumarie's modified Riemann…

Purpose This paper aims to present a numerical solution of non‐linear Burger's equation using differential quadrature method based on sinc functions. Design/methodology/approach Sinc Differential Quadrature Method is used for space discretization and four stage Runge‐Kutta algorithm is used for time discretization. A…