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 present a numerical approach to solving singularly perturbed semilinear convection-diffusion problems. The nonlinear part of the problem is linearized via quasilinearization technique. We then design and implement fitted operator finite difference method solve sequence linear problems that emerges from process. carry out rigorous analysis attest convergence proposed procedure ...

and Applied Analysis 3 Table 1 Quasilinearization method Integer derivative Caputo’s derivative Monotone sequences Yes Yes Unique solution exists Yes Yes Uniform convergence Yes Yes Quadratic semiquadratic convergence Yes Yes Then, α0 ≤ β0 0, where α0 α0 t t − t0 |t t0 and β0 0 β0 t t − t0 |t t0 imply that α0 t ≤ β0 t , t0 ≤ t ≤ T. Corollary 2.2. The function F t, u σ t u, where σ t ≤ L, is adm...