This paper considers approximate solution of the hyperbolic one-dimensional wave equation with nonlocal mixed boundary conditions by improved methods based on the assumption that the solution is a double power series based on orthogonal polynomials, such as Bernstein, Legendre, and Chebyshev. The solution is ultimately compared with the original method that is based on standard polynomials by calculating the absolute error to verify the validity and accuracy of the performance.

     The primary objective of the current paper is to suggest and implement effective computational methods (DECMs) to calculate analytic and approximate solutions to the nonlocal one-dimensional parabolic equation which is utilized to model specific real-world applications. The powerful and elegant methods that are used orthogonal basis functions to describe the solution as a double power series have been developed, namely the Bernstein, Legendre, Chebyshev, Hermite, and Bernoulli polynomials. Hence, a specified partial differential equation is reduced to a system of linear algebraic equations that can be solved by using Mathematica®12. The techniques of effective computational methods (DECMs) have been applied to solve some s

The introduction and importance of the research included that physical education and its various activities are important for the disabled. The exercise of physical activities by the disabled effectively contributes to raising their level of fitness and reducing diseases caused by lack of movement. Disabled people often suffer from psychological and social problems, and this feeling may be accompanied by a high level of anxiety, a lack of self-esteem and a loss of self-confidence. Psychological adaptation is one of the concepts of sports psychology interconnected with the psychological climate, as the process that the player seeks to meet his demands and needs. Adaptation includes the pursuit of emotional balance between the individual play

In our article, three iterative methods are performed to solve the nonlinear differential equations that represent the straight and radial fins affected by thermal conductivity. The iterative methods are the Daftardar-Jafari method namely (DJM), Temimi-Ansari method namely (TAM) and Banach contraction method namely (BCM) to get the approximate solutions. For comparison purposes, the numerical solutions were further achieved by using the fourth Runge-Kutta (RK4) method, Euler method and previous analytical methods that available in the literature. Moreover, the convergence of the proposed methods was discussed and proved. In addition, the maximum error remainder values are also evaluated which indicates that the propo

Proxy-based sliding mode control PSMC is an improved version of PID control that combines the features of PID and sliding mode control SMC with continuously dynamic behaviour. However, the stability of the control architecture maybe not well addressed. Consequently, this work is focused on modification of the original version of the proxy-based sliding mode control PSMC by adding an adaptive approximation compensator AAC term for vibration control of an Euler-Bernoulli beam. The role of the AAC term is to compensate for unmodelled dynamics and make the stability proof more easily. The stability of the proposed control algorithm is systematically proved using Lyapunov theory. Multi-modal equation of motion is derived using the Galerkin metho

Cryptosporidiosis is mainly cause a persistent diarrhea in immune compromised patients, BALB/c mice have been suppressed by dexamethasone, tissue Th1, Th2 and Th17 cytokines concentrations in the ileum were significantly diminished in both infected and immunosuppressed mice. Level of IFN-g, TNF-a, IL-12, IL-6, IL-17A was increased in level, IL-4 didn’t increases, in both ileal and spleen tissue. Levels of above cytokines were examined in spleen in order to follow the proliferation of CD4+ T-cell during C. parvum infection.