Abstract Brain neural networks are regarded as dynamical systems in science, which memories interpreted attractors of the systems. Mathematically, ordinary differential equations (ODEs) can be utilized to describe Any ODE that is employed dynamics a network called neuralODE. Inspired by rethinking nonlinear representation ability existing artificial together with functions columns neocortex, th...

t. ikawa obtained an ordinary differential equation for the circular helix. recently, the helix havebeen investigated by many differential geometers such as t. ikawa, h. balgetir, m. bektas, m. ergut, n.ekmekci and h. h. hacısalihoglu. in this paper, making use of this author’s methods, we obtainedcharacterizations of helix for a curve with respect to the frenet frame in 3-dimensional galilean ...

in this paper, the chebyshev spectral collocation method(cscm) for one-dimensional linear hyperbolic telegraph equation is presented. chebyshev spectral collocation method have become very useful in providing highly accurate solutions to partial differential equations. a straightforward implementation of these methods involves the use of spectral differentiation matrices. firstly, we transform ...

the numerical methods are of great importance for approximating the solutions of nonlinear ordinary or partial differential equations, especially when the nonlinear differential equation under consideration faces difficulties in obtaining its exact solution. in this latter case, we usually resort to one of the efficient numerical methods. in this paper, the chebyshev collocation method is sugge...

In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.). So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreo...

Although Elzaki transform is stronger than Sumudu and Laplace transforms to solve the ordinary differential equations withnon-constant coefficients, but this method does not lead to finding the answer of some differential equations. In this paper, a method is introduced to find that a differential equation by Elzaki transform can be ‎solved?‎

the extended homogeneous balance method is used to construct exacttraveling wave solutions of the maccari system, in which thehomogeneous balance method is applied to solve the riccati equationand the reduced nonlinear ordinary differential equation. many exacttraveling wave solutions of the maccari system equation aresuccessfully obtained.