We propose a new modification of Bellman’s quasilinearization method such that at any iteration step, it works with an approximate solution of the original nonlinear system and with new approximation of parameters α(k+1) which are close enough to the previous ones. As an output, this approach provides a construction of a convergent sequence of parameters where the limit is the best approximatio...

This article deals the Hall and ion slip currents on free convection flow, heat and mass transfer of an electrically conducting couple stress fluid through porous channels with chemical reaction, Soret and Dufour effects. Assume that there is symmetric suction or injection along the expanding or contracting walls, which are maintained at different constant temperatures and concentrations. The g...

The analysis of heat conduction through a solid with heat generation leads to a linear matrix differential equation with separated boundary conditions. We present a symmetric second order exponential integrator for the numerical integration of this problem using the imbedding formulation. An algorithm to implement this explicit method in an efficient way with respect to the computational cost o...

Correspondence: [email protected]. tr Department of Statistics, Gaziosmanpasa University, Tasliciftlik Campus, 60250 Tokat, Turkey Abstract This paper deals with an application of the method of quasilinearization by not demanding the Hölder continuity assumption of functions involved and by choosing upper and lower solutions with initial time difference for nonlinear Caputo fractional different...

Existence and approximation of solutions for a class of boundary value problems on time scales of the type − [p(t)y∆(t)]∇ + q(t)y(t) = f(t, y(t)), t ∈ [a, b]T, c1y(ρ(a))− c2y(ρ(a)) = 0, d1y(b) + d2y(b) = 0, is established. For the existence theory, we develop the method of upper and lower solutions. To approximate the solution, we develop the generalized method of quasilinearization. We show th...

In this paper, we study existence and approximation of solutions to some threepoint boundary value problems for fractional differential equations of the type Dq 0+u(t) + f(t, u(t)) = 0, t ∈ (0, 1), 1 < q < 2 u′(0) = 0, u(1) = ξu(η), where 0 < ξ, η ∈ (0, 1) and Dq 0+ is the fractional derivative in the sense of Caputo. For the existence of solution, we develop the method of upper and lower solut...