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- Katarina Surla, Ljiljana Teofanov, Zorica Uzelac
- Applied Mathematics and Computation
- 2009

The singularly perturbed parabolic boundary value problem is considered. Difference scheme is obtained by using cubic spline difference scheme on Shishkin’s mesh in space and classical discretization on uniform mesh in time. To obtain better stability and simpler matrix the fitting factor in polynomial form is used. The uniform convergence is achieved.… (More)

We consider a spline difference scheme on a piecewise uniform Shishkin mesh for a singularly perturbed boundary value problem with two parameters. We show that the discrete minimum principle holds for a suitably chosen collocation points. Furthermore, bounds on the discrete counterparts of the layer functions are given. Numerical results indicate uniform… (More)

- Katarina Surla, Vanja Vukoslavčević
- 2002

Two uniformly stable difference schemes for the singularly perturbed parabolic boundary value problem are derived. Numerical results indicate the uniform convergence. AMS Mathematics Subject Classifications (2000): 65L10

The linear singularly perturbed reaction-diffusion problem is considered. The spline difference scheme on the Shishkin mesh is used to solve the problem numerically. With the special position of collocation points, the obtained scheme satisfies the discrete minimum principle. Numerical experiments which confirm theoretical results are presented. AMS… (More)

A semilinear singularly perturbed reaction-diffusion problem is considered and the approximate solution is given in the form of a quadratic polynomial spline. Using the collocation method on a simple piecewise equidistant mesh, an approximation almost second order uniformly accurate in small parameter is obtained. Numerical results are presented in support… (More)

- Zorica Uzelac, Katarina Surla
- Int. J. Comput. Math.
- 1999

- Katarina Surla, Zorica Uzelac, Ljiljana Teofanov
- Mathematics and Computers in Simulation
- 2009

In this paper the quadratic spline difference scheme for a convection-diffusion problem is derived. With the suitable choice of collocation points we provide the discrete minimum principle. The numerical results implies the uniform convergence of order O(n−2 ln n).

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