A block Newton’s method for computing invariant pairs of nonlinear matrix pencils

The block inverse iteration and block Newton’s methods proposed by the authors of this paper for computing invariant pairs of regular linear matrix pencils are generalized to the case of regular nonlinear matrix pencils. Numerical properties of the proposed methods are demonstrated with a typical quadratic eigenproblem.

Fixed Point and Newton’s Methods in the Complex Plane

We revisit the necessary and sufficient conditions for linear and high order of convergence of fixed point and Newton’s methods in the complex plane. Schröder’s processes of the first and second kind are revisited and extended. Examples and numerical experiments are included.

Thermal Radiation Effect on 3D Slip Motion of Alcu-Water and Cu-Water Nanofluids over a Variable Thickness Stretched Surface

The current paper covers the examination of 3D nanofluid motion over a slendering expanding sheet under the influence of slip effect and thermal radiation. In this study, we considered the Cu-water and Al50Cu50-water nanofluids over a non-uniform thickness expanding sheet. With the help of similitude transformations, we changed the derived governed equations as ordinary differential equations. The mathematical outcomes determined by using Runge-Kutta and Newton’s methods. We reveal and interpret the graphs for different parameters of interest. We discussed the skin friction coefficient and reduced Nusselt number at different pertinent parameters. Results shown that the rate of heat transfer is higher in Al50Cu50-water nanofluid when compared with Cu-water nanofluid.