A numerical solution for nonlinear heat transfer of fin problems using the Haar wavelet quasilinearization method

The aim of this paper is to study the new application of Haar wavelet quasilinearization method (HWQM) to solve one-dimensional nonlinear heat transfer of fin problems. Three different types of nonlinear problems are numerically treated and the HWQM solutions are compared with those of the other method. The effects of temperature distribution of a straight fin with temperature-dependent thermal conductivity in the presence of various parameters related to nonlinear boundary value problems are analyzed and discussed. Numerical results of HWQM gives excellent numerical results in terms of competitiveness and accuracy compared to other numerical methods. This method was proven to be stable, convergent and, easily coded

Numerical solution of the inverse Gardner equation

In this paper, the numerical solution of the inverse Gardner equation will be considered. The Haar wavelet collocation method (HWCM) will be used to determine the unknown boundary condition which is estimated from an over-specified condition at a boundary. In this regard, we apply the HWCM for discretizing the space derivatives and then use a quasilinearization technique to linearize the nonlinear term in the equations. It is proved that the proposed method has the order of convergence O(∆x). The efficiency and robustness of the proposed approach for solving the inverse Gardner equation are demonstrated by one numerical example.Publisher's Versio

Using a cubic B-spline method in conjunction with a one-step optimized hybrid block approach to solve nonlinear partial differential equations

[EN] In this paper, we develop an optimized hybrid block method which is combined with a modified cubic B-spline method, for solving non-linear partial differential equations. In particular, it will be applied for solving three well-known problems, namely, the Burgers equation, Buckmaster equation and FitzHugh–Nagumo equation. Most of the developed methods in the literature for non-linear partial differential equations have not focused on optimizing the time step-size and a very small value must be considered to get accurate approximations. The motivation behind the development of this work is to overcome this trade-off up to much extent using a larger time step-size without compromising accuracy. The optimized hybrid block method considered is proved to be A-stable and convergent. Furthermore, the obtained numerical approximations have been compared with exact and numerical solutions available in the literature and found to be adequate. In particular, without using quasilinearization or filtering techniques, the results for small viscosity coefficient for Burgers equation are found to be accurate. We have found that the combination of the two considered methods is computationally efficient for solving non-linear PDEs.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature.Publicación en abierto financiada por el Consorcio de Bibliotecas Universitarias de Castilla y León (BUCLE), con cargo al Programa Operativo 2014ES16RFOP009 FEDER 2014-2020 DE CASTILLA Y LEÓN, Actuación:20007-CL - Apoyo Consorcio BUCL

A numerical solution for heat transfer past a stretching sheet with ohmic dissipation and suction or injection problem using Haar wavelet quasilinearization method

This paper represents a numerical analysis for heat transfer of a Jeffrey fluid flow past a stretching sheet with ohmic dissipation and suction/injection. The partial differential equations are reduced into a set of convenient nonlinear ordinary differential equations with the boundary conditions. Haar wavelet quasilinearization method (HWQM) is used to solve ordinary differential equations. The effect of various related parameters on velocity and temperature profiles are computed and analyzed. Then, comparison is made between the numerical results of proposed method with existing numerical solutions found in the literature, and reasonable agreement is noted

Neuro-swarm computational heuristic for solving a nonlinear second-order coupled Emden–Fowler model

The aim of the current study is to present the numerical solutions of a nonlinear second-order coupled Emden–Fowler equation by developing a neuro-swarming-based computing intelligent solver. The feedforward artificial neural networks (ANNs) are used for modelling, and optimization is carried out by the local/global search competences of particle swarm optimization (PSO) aided with capability of interior-point method (IPM), i.e., ANNs-PSO-IPM. In ANNs-PSO-IPM, a mean square error-based objective function is designed for nonlinear second-order coupled Emden–Fowler (EF) equations and then optimized using the combination of PSO-IPM. The inspiration to present the ANNs-PSO-IPM comes with a motive to depict a viable, detailed and consistent framework to tackle with such stiff/nonlinear second-order coupled EF system. The ANNs-PSO-IP scheme is verified for different examples of the second-order nonlinear-coupled EF equations. The achieved numerical outcomes for single as well as multiple trials of ANNs-PSO-IPM are incorporated to validate the reliability, viability and accuracy.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. The authors have not disclosed any funding