An investigation is conducted into how radiation affects the non-Newtonian second-grade fluid in double-diffusive convection over a stretching sheet. When fluid is flowing through a porous material, the Lorentz force and viscous dissipation are also taken into account. The flow equations are coupled partial differential equations that can be solved by MATLAB’s built-in bvp4c algorithm after being transformed into ODEs using appropriate similarity transformations. Utilizing graphs and tables, the impact of a flow parameter on a fluid is displayed. On velocity, temperature, and concentration profiles, the effects of the magnetic field, Eckert number, and Schmidt number have been visually represented. Calculate their inaccuracy by comparing the Nusselt number and Sherwood number values to those from earlier investigations.

This paper is devoted to the discussion of dynamical properties of anisotropic dark energy cosmological model of the universe in a Bianchi type-V space time in the framework of scale covariant theory of gravitation formulated by Canuto et al.(phys.Rev.Lett.39:429,1977).A  dark energy cosmological model is presented by solving the field equations of this theory by using some physically viable conditions. The dynamics of the model is  studied  by computing the cosmological parameters, dark energy density, equation of state(EoS) parameter, skewness parameters, deceleration parameter and the jerk parameter. This being a scalar field model gives us the quintessence model of the universe which describes a significant dark energy candidate of our accelerating universe. All the physical quantities discussed are in agreement with the recent cosmological observations.

This paper is concerned with the numerical solution of the mixed Volterra-Fredholm integral equations by using a version of the block by block method. This method efficient for linear and nonlinear equations and it avoids the need for spacial starting values. The convergence is proved and finally performance of the method is illustrated by means of some significative examples.