An optimal iterative algorithm for solving Bratu-type problems

An optimal sixth‐order quartic B‐spline collocation method for solving Bratu‐type and Lane‐Emden–type problems

“…Das et al 4 proposed a modified version of the variational iteration method to obtain series solution of problems (1) and (2). Moreover, Roul and Madduri 13 used an optimal homotopy analysis method (OHAM) to solve Bratu-type problem.…”

Some Numerical and Analytical Solutions to an Enzyme-Substrate Reaction-Diffusion Problem

“…The Euler method (28)-(29) is a first order accurate method. There are many other Runge-Kutta type methods for solving system (26)- (27) with higher order accuracy, such as the second order Heun's method, third order Runge-Kutta method, fourth order Runge-Kutta method, and fifth order Dormand-Prince method. The later is a famous one due to Dormand and Prince [47] which is implemented in the MATLAB software as the ode45 algorithm [48,49].…”

“…The unsaturated and saturated steady state solutions to the initial value problem have been obtained by Rahamathunissa and Rajendran [10] using a variational iteration method. The variational iteration method was due to He [12,13,14] and it has been successfully used to solve various problems [15,16,17,18,19,20,21,22,23,24] including the mathematical chemistry areas [25,26,27,28,29,30].…”

Numerical solution of Bratu’s and related problems using a third derivative hybrid block method

“…The numerical outcomes with the proposed OHBM are compared with those provided with the VIM method in Das et al (2016) and the OIA method in Roul and Madduri (2019). It can be seen from Tables 1 and 2 that the absolute errors (AE) obtained with our present method are more accurate than those with the methods in Das et al (2016) and Roul and Madduri (2019) where this problem has been solved using the same values of step-size (h). Comparison of the exact versus numerical solution is displayed in Fig.…”