Cristina B. Corcino^1,2, Wilson D. Castañeda Jr.³, Roberto B. Corcino^1,2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.132, No.1, pp. 133-151, 2022, DOI:10.32604/cmes.2022.019965 - 02 June 2022

Abstract The tangent polynomials T_n (z) are generalization of tangent numbers or the Euler zigzag numbers T_n. In particular, T_n (0) = T_n. These polynomials are closely related to Bernoulli, Euler and Genocchi polynomials. One of the extensions and analogues of special polynomials that attract the attention of several mathematicians is the Apostoltype polynomials. One of these Apostol-type polynomials is the Apostol-tangent polynomials T_n(z, λ). When λ = 1, T_n (z, 1) = T_n(z). The use of hyperbolic functions to derive asymptotic approximations of polynomials together with saddle point method was applied to the Bernoulli and Euler polynomials by Lopez… More >

A. Shahzad¹, W. A. Khan^2,*, R. Gul¹, B. Dayyan¹, M. Zubair¹

CMC-Computers, Materials & Continua, Vol.68, No.3, pp. 3877-3893, 2021, DOI:10.32604/cmc.2021.012524 - 06 May 2021

Abstract In this work, a steady, incompressible Williamson fluid model is investigated in a porous wavy channel. This situation arises in the reabsorption of useful substances from the glomerular filtrate in the kidney. After 80% reabsorption, urine is left, which behaves like a thinning fluid. The laws of conservation of mass and momentum are used to model the physical problem. The analytical solution of the problem in terms of stream function is obtained by a regular perturbation expansion method. The asymptotic integration method for small wave amplitudes and the RK-Fehlberg method for pressure distribution has been… More >