Diffusion problems with a mixed nonlinear boundary condition

Wavelet Galerkin method for solving nonlinear singular boundary value problems arising in physiology

“…A similar equation for r ¼ 2 arise in the study of the distribution of heat sources in the human head [23,24], in which: f ðx; yÞ ¼ f ðyÞ ¼ Àl expðÀlkyÞ; l > 0; k > 0:…”

A collection of computational techniques for solving singular boundary-value problems

“…With non-linear boundary conditions, existence and uniqueness for this problem has been established in [37] at x = 1. Solution of this problem is given by two methods, the second-order finite difference methods based on a uniform mesh and based on a non uniform mesh, which extends the method M 1 and M 2 developed by Chawla and Katti [17] for pðxÞ ¼ x b 0 ; 0 6 b 0 < 1, and with boundary conditions y(0) = A, y(1) = B.…”

“…It is assumed that the problem satisfy all the properties of [5] for x 2 [0, 1]. A similar problem arises in the study of the distribution of heat sources in the human head for f(x, y) = Àne Ànk , n > 0, k > 0 in [28,37]. Direct method based on cubic spline approximation for a class of singular problem arising in physiology has been discussed and initially the given non-linear problem reduced to a linear problem using quasilinearization technique.…”

On the convergence of a fourth-order method for a class of singular boundary value problems

“…The existence-uniqueness of the solution of the boundary value problem (1) and (2) is established in [16,17] for xp /p analytic in {x : |x| < r} for some r > 1 and for the more general problem in [8] with nonlinear boundary conditions. The boundary value problem (1) and (2) with b 0 = 0, 1, 2 and q (x) = 1 arises in the study of various tumor growth problems [1][2][3]9] with linear f (x, y) and also with non-linear f (x, y) of the form f (x, y) ≡ f (y) = θ y/(y + κ), θ > 0, κ > 0.…”