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 paper presents the impedance measurement method using a real-life step pulse as a perturbation signal and Laplace transformation as a tool for analyzing the response of the object under test. The method is addressed to explore different technical object (like anticorrosion coatings, gas sensors, ceramics, dielectrics biological tissues etc.) when the measurement time cannot be long. The pre...

in this paper, a reliable approach is introduced to approximate periodic solutions of a system of coupled integrable dispersionless. the system is firstly, transformed into an ordinary differential equation by wave transformation. the solution of ode is obtained by the homotopy perturbation method. to show the periodic behavior of the solution, a modification based on the laplace transforms and...

In this study, a step process of semi-Markovian random walk with delaying barriers at  a and  b levels ( 0   b a ) and first falling moment of the process into the delaying barrier at b -level, ) ( , are mathematically constructed, in this case when the random walk happens according to the Laplace’s distribution ) 1 ; 1 (   L . It is given a simple form of the Laplace transformation of t...

Abstract In this paper, a new form of the homotopy perturbation method (NHPM) has been adopted for solving integro-differential equations. In the present study, firstly the NHPM is used to the integro-differential equation, which yields the Maclaurin series of the exact solution. By applying the Laplace transformation to the truncated Maclaurin series and then the Padé approximation to the solu...

The generalized coupled thermo-viscoelasticity of hollow sphere subjected to thermal symmetric shock load is presented in this paper. To overcome the infinite speed of thermal wave propagation, the Lord-Shulman theory is considered. Two coupled equations, namely, the radial equation of motion and the energy equation of a hollow sphere are obtained in dimensionless form. Resulting equations are ...

A new generalized function space in which all Gelfand-Shilov classes S ′0 α (α > 1) of analytic functionals are embedded is introduced. This space of ultrafunctionals does not possess a natural nontrivial topology and cannot be obtained via duality from any test function space. A canonical isomorphism between the spaces of hyperfunctions and ultrafunctionals on R is constructed that extends the...

We investigate the effectiveness of Inverse Laplace Transform (ILT) analysis method to extract distribution relaxation rates from nuclear magnetic resonance data with stretched exponential relaxation. Stretched-relaxation is a hallmark rates, and an analytical expression exists for this case spin-1/2 nucleus. compare theoretical those extracted via ILT several values stretching exponent at diff...