The aim of this paper is to present the numerical method for solving linear system of Fredholm integral equations, based on the Haar wavelet approach. Many test problems, for which the exact solution is known, are considered. Compare the results of suggested method with the results of another method (Trapezoidal method). Algorithm and program is written by Matlab vergion 7.

Due to the importance of solutions of partial differential equations, linear, nonlinear, homogeneous, and non-homogeneous, in important life applications, including engineering applications, physics and astronomy, medical sciences, and life technology, and their importance in solutions to heat transfer equations, wave, Laplace equation, telegraph, etc. In this paper, a new double integral transform has been proposed.

In this work, we have introduced a new double transform ( Double Complex EE Transform ). In addition, we presented the convolution theorem and proved the properties of the proposed transform, which has an effective and useful role in dealing with the solution of two-dimensional partial differential equations. Moreover

In this paper, a new analytical method is introduced to find the general solution of linear partial differential equations. In this method, each Laplace transform (LT) and Sumudu transform (ST) is used independently along with canonical coordinates. The strength of this method is that it is easy to implement and does not require initial conditions.

This paper proposes a novel finite-time generalized proportional integral observer (FTGPIO) based a sliding mode control (SMC) scheme for the tracking control problem of high order uncertain systems subject to fast time-varying disturbances. For this purpose, the construction of the controller consists of two consecutive steps. First, the novel FTGPIO is designed to observe unmeasurable plant dynamics states and disturbance with its higher time derivatives in finite time rather than infinite time as in the standard GPIO. In the FTGPO estimator, the finite time convergence rate of estimations is well achieved, whereas the convergence rate of estimations by classical GPIO is asymptotic and slow. Secondly, on the basis of the finite and fast e

In this paper, the Decomposition method was used to find approximation solutions for a system of linear Fredholm integral equations of the second kind. In this method the solution of a functional equations is considered as the sum of an infinite series usually converging to the solution, and Adomian decomposition method for solving linear and nonlinear integral equations. Finally, numerical examples are prepared to illustrate these considerations.

Numerous tests are recently conducted to assess vibration's role in accelerating the heat transfer rate in various heat exchangers. In this work, the enhancement of heat transfer by the effect of transfer vibration and inclination angles on the surface of a double pipe heat exchanger experimentally has been investigated. A data acquisition system is applied to record the data of temperatures, flow rates, and frequencies over the tests. A compound technique was adopted, including the application of a set of inclination angles of (0°, 10°, 20°, and 30°) under the effect of frequency of vibration ranging from sub-resonance to over-resonance frequencies. The results showed that the overall heat transfer coefficient enhan

Inherent fluctuations in the availability of energy from renewables, particularly solar, remain a substantial impediment to their widespread deployment worldwide. Employing phase-change materials (PCMs) as media, saving energy for later consumption, offers a promising solution for overcoming the problem. However, the heat conductivities of most PCMs are limited, which severely limits the energy storage potential of these materials. This study suggests employing circular fins with staggered distribution to achieve improved thermal response rates of PCM in a vertical triple-tube heat exchanger involving two opposite flow streams of the heat-transfer fluid (HTF). Since heat diffusion is not the same at various portions of the PCM unit,