... are reduced through similarity transformations to a coupled nonlinear system of ordinary differential equations. The resulting boundary-value problem is solved in MATLAB using the bvp4c collocation solver, and the numerical accuracy is assessed through residual, grid-refinement, convergence and validation...

... effective. Finally, convergence of HPM is proved strictly with detail. Findings It is not necessary to consider any type of assumptions and hypothesis for the development of this approach. Thus, the suggested method becomes very simple and a better approach for the solution of time-fractional...

... the uniqueness condition. Stability and convergence of numerical solutions in Newton and Stokes’ iterative schemes are also analyzed under some strong uniqueness conditions. Findings This work was supported by the NSF of China (No. 11971152). Originality/value This paper presents the best choice...

...Christopher DeGroot Purpose This paper aims to investigate the convergence and error properties of a finite volume-based heat conduction code that uses automatic differentiation to evaluate derivatives of solutions outputs with respect to arbitrary solution input(s). A problem involving conduction...

... with fully implicit (FI) discretization used to acquire accurate simulation. A Picard–Newton (PN) iteration with a quadratic convergent ratio is designed to realize fast solution. Theoretical analysis is performed using the discrete function analysis technique. By adopting a novel induction hypothesis...

... of the dependent variable in the parabolic PDE for the evaluation of the time derivative. As will be demonstrated later, this key step is responsible for improving the accuracy of ITMOL over its predecessor TMOL. Throughout the paper, the theoretical properties of ITMOL, such as consistency, stability, convergence...

.... Findings – The series solution of the MHD flow of an incompressible viscous fluid over a non-linear stretching sheet subject to slip condition is obtained. An excellent agreement between the MLDM and HPM is achieved. Convergence of the obtained series solution is properly checked by using the ratio test...

... target temperature field. The control aspects are discussed and we summarize convergence results. Numerical results for a test problem are included to illustrate the approach. If β<αC², then Equation 16 and for the case t_*=∞, L²(Ω...

...H. Lai; Y.Y. Yan In this paper the effects of choosing dependent variables and cell face velocities on convergence of the SIMPLE algorithm are discussed. Using different velocity components as either dependent variables or cell‐face velocities, both convergent rate and calculation accuracy...