Sections 3 and 4 deal with the construction of the implicit finite

difference methods, the theorems on existence, uniqueness of solutions to the suitable difference schemes and some convergence and stability properties in the one and two-dimensional cases, respectively.

It addresses convection-diffusion problems in one and two dimensions, finite

difference methods in one and two dimensions, and finite element methods.

A novel technique of finite

difference methods is proposed.

[26]--, Finite

difference methods for computing eigenvalues of fourth order boundary value problems, Internat.

Morton,

Difference Methods for Initial-Value Problems, Interscience Tracts in Pure and Applied Mathematics, No.

George, "On the use of high order

difference methods for the system of one space second order non-linear hyperbolic equations with variable coefficients," Journal of Computational and Applied Mathematics, vol.

Thomee, Finite

Difference Methods for Linear Parabolic Equations, Elsevier Science Publishers B.V.

Adel, "On the stability analysis of weighted average finite

difference methods for fractional wave equation," Fractional Differential Calculus, vol.

To conclude, in this paper, we have reviewed and restudied some latest adaptive, semi-adaptive finite

difference methods for solving a degenerate Kawarada equation problem.

1979), Monte Carlo simulation (Boyle 1977), implicit finite difference and explicit finite

difference methods are also described and documented.

Morton,

Difference Methods for Initial Value Problems, 2nd edn.

Generally, at the use of finite

difference methods curvilinear boundary between media is replaced by a step approximating surface [6].