A Modified Spectral Relaxation Method for Some Emden-Fowler Equations

In this chapter, we present a modified version of the spectral relaxation method for solving singular initial value problems for some Emden-Fowler equations. This study was motivated by the several applications that these equations have in Science. The first step of the method of solution makes use of linearisation to solve the model problem on a small subinterval of the problem domain. This subinterval contains a singularity at the initial instant. The first step is combined with using the spectral relaxation method to recursively solve the model problem on the rest of the problem domain. We make use of examples to demonstrate that the method is reliable, accurate and computationally efficient. The numerical solutions that are obtained in this chapter are in good agreement with other solutions in the literature.

Peer influence and sexual debut : A mathematical approach

Objectives: Early sexual debut is one of the major causes of STIs and unwanted pregnancy. A deterministic mathematical model to attempt to understand the role of prostitution and peer influence on early sexual debut is developed and analyzed. Results: The thresholds known as the reproduction number and equilibria for the model are determined and stabilities analyzed. Analysis of the reproduction number suggests that prostitution and economic hardships enhance early sexual debut. Sensitivity analysis of the reproduction number is carried out and it suggests that a reduction in prostitution has the greatest impact in reducing the reproduction number. Using the multi-domain pseudo-spectral relaxation method (MD-SRM), numerical simulations are carried out. Numerical simulations suggest that prostitution and peer influence enhances early sexual debut.

Thermal Slip Flow of a Three-Dimensional Casson Fluid Embedded in a Porous Medium with Internal Heat Generation

Present assessment is considered to analysis flow as well as heat characteristics of steady, thermal slip flow of three-dimensional Casson fluid embedded in a porous medium with internal heat generation. Geometry of the present analysis is linearly stretched surface. Later, all the PDEs corresponding to the study are altered to set of nonlinear equations ODEs by means of appropriate similarity transformations. An efficient numerical scheme of spectral relaxation method (SRM) is applied to solve the nonlinear ordinary system. Variations of Nusselt number, temperature, velocity, and local skin friction coefficient with fluid parameters exhibited by graphs and tables. Spectral relaxation method gives an exact convergence to the nonlinear boundary value problems compare with general methods. In this study, to improve the precision and accuracy of the SRM successive over-relaxation (SOR) strategy is utilized. Proposed method as well as outcomes is checked with the comparison. A sensible connection is acquired between the current outcomes and accessible outcomes in writing. Some of the observations are skin friction coefficient raises and velocities decreases by the magnetic field strength. Skin friction and Local Nusselt number at the surface is more pronounced for non-Newtonian case than that of Newtonian case.

A Numerical Examination of an Unsteady Nonlinear MHD Flow in the Presence of Thermal Radiation and Heat Generation

In this study, the spectral perturbation method and the spectral relaxation method are used to solve the nonlinear differential equations of an unsteady nonlinear MHD flow in the presence of thermal radiation and heat generation. The SPM is mainly based on series expansion, generating series approximation coupled with the Chebyshev spectral method. The numerical results generated using the spectral perturbation method were compared with those found in the literature, and the two results were in good agreement.

Numerical Analysis of MHD Stagnation Point Flow Towards a Radially Stretching Convectively Heated Disk

The steady stagnation point flow and heat transferof an electrically conducting incompressible viscous fluid isextended to the case where the disk surface is convectivelyheated and radially stretching. The fluid is subjected to anexternal uniform magnetic field perpendicular to the planeof the disk. The governing momentum and energy balanceequations give rise to non-linear boundary value problem.Using a spectral relaxation method with a Chebyshev spectralcollocation method, the numerical solutions are obtained overthe entire range of the physical parameters. Emphasis hasbeen laid to study the effects of viscous dissipation and Jouleheating on the thermal boundary layer. Pertinent results on theeffects of various thermophysical parameters on the velocityand temperature fields as well as local skin friction and localNusselt number are discussed in detail and shown graphicallyand/or in tabular form.