A monotonicity procedure for the accurate, efficient solution of certain heat-transfer problems with variable thermal properties
The work is dedicated to the numerical solution of the nonlinear boundary value problem \[ a(F) F'' + b(F) (F')^2 = f(F),\;F = F(x), \;0 < x < 1;\;F'(0) = 0,\;F(1) = K = \text{const} > 0. \] Particular cases of this problem are discussed and studied. For them the Newton/Picard iterative schemes are presented; their convergence is proved. The peculiarities of the solutions of the discussed problems are stated. The discretization of the iterative schemes is carried out and the question of their stability is discussed. Results of numerical experiments of solving model examples with various initial data are presented. They are compared with the initial solutions obtained by other authors.
scientific article; zbMATH DE number 777856