In this paper, we apply the homotopy perturbation method (HPM), modified method(MHPM), variational iteration (VIM), Adomian decomposition (ADM), and (MADM) to solve nonlinear mixed Volterra-Fredholm integral equations itssystem. We investigate approximate solution of equation its system via proposed methods. Thevalidity efficiency these methods are demonstrated through various numerical example...

in recent years, numerous approaches have been applied for finding the solutions of functional equations. one of them is the optimal homotopy asymptotic method. in current paper, this method has been applied for obtaining the approximate solution of fisher equation. the reliability of the method will be shown by solving some examples of various kinds and comparing the obtained outcomes with the ...

in this paper a new form of the homptopy perturbation method is used for solving oscillator differential equation, which yields the maclaurin series of the exact solution. nonlinear vibration problems and differential equation oscillations have crucial importance in all areas of science and engineering. these equations equip a significant mathematical model for dynamical systems. the accuracy o...

The manuscript solves a modified Kawahara equation (mKE) within two cases with and without damping term by applying the Laplace homotopy perturbation method (LHPM). Since damped mKE is non-integrable (i.e., it does not have analytic integrals) exact initial conditions, this challenge makes many numerical methods fail to solve equations. In article, we suggested new modification at LHPM setting ...

We compare Friedlander’s definition of étale homotopy for simplicial schemes to another definition involving homotopy colimits of pro-simplicial sets. This can be expressed as a notion of hypercover descent for étale homotopy. We use this result to construct a homotopy invariant functor from the category of simplicial presheaves on the étale site of schemes over S to the category of pro-spaces....