"This volume is the Proceedings of the First Conference on Finite Difference Methods which was held at the University of Rousse, Bulgaria, August 10-13, 1997"--Preface.

Includes bibliographical references and index.

Ch. 1. Weak Smoothness Conditions and the Newton's Method / Vasile Berinde -- Ch. 2. Josephson Lattices Having an Optimal Sizes / Todor L. Boyadjiev and Nora V. Alexeeva -- Ch. 3. Difference Scheme for Singularly Perturbed Reaction-Diffusion Problems with Concentrated Capacity / Ilia A. Braianov and Lubin G. Vulkov -- Ch. 4. An Efficient Numerical Technique for Simulating 3D Technological Solidification Processes / T. P. Chernogorova and O. P. Iliev -- Ch. 5. Parallel Algorithms of Domain Decomposition to Solve the Navier-Stokes Equations / Vladimir V. Chudanov, Alexander G. Churbanov and Andrei N. Pavlov / [et al.] -- Ch. 6. Mathematical modelling of impurity in grain boundary neighborhood in a dislocation wall force field (modified Fisher model) / M. M. Chuiko, A. K. Fedotov and V. G. Rychagov -- Ch. 7. Finite-difference Methods for Solving a Non-linear Chemical Oscillator Problem / Z. Cinar and E. H. Twizell -- Ch. 8. On a Fitted Operator Technique for Singular Perturbation Equations / P. A. Farrell, A. Hegarty and J. J. H. Miller / [et al.] -- Ch. 9. Some New Discretizations of Evolution Equations / I. P. Gavrilyuk -- Ch. 10. A Constructive Representation of the Solution of a First Order Differential Equation with a Non-constant Operator Coefficient in Banach Spaces and Applications / I. P. Gavrilyuk, V. L. Makarov and I. S. Kravez -- Ch. 11. Stability of Symmetrizable Difference Schemes / Alexei V. Goolin -- Ch. 12. On Numerical Solution of 3D Navier-Stokes Equations in Vorticity-Vector Potential Formulation / O. P. Iliev, P. Stankov and D. M. Stoyanov -- Ch. 13. Third Order Fractional Step Methods For Multidimensional Evolutionary Convection-Diffusion Problems / J. C. Jorge and B. Bujanda -- Ch. 14. Simplified 3D Magnetospheric Magnetic Field / D. K. Koitchev, M. S. Kaschiev and M. D. Kartalev -- Ch. 15. A Finite Difference Scheme for Computation of the Logarithmic Potential / Natalia Kolkovska -- Ch. 16. Implicit Difference Methods for a Non-linear Heat Equation with Functional Dependence / Henryk Leszczynski -- Ch. 17. Numerical Solution of a Bilateral Constrained Junction Problem / P. A. Lotito, G. F. Reyero and R. L. V. Gonzalez -- Ch. 18. Difference Schemes on Nonuniform Grids for Multi-dimensional Equations / P. P. Matus -- Ch. 19. L[subscript 2]-Conservative Difference Schemes for the Korteweg-de Vries Equation / P. P. Matus, V. I. Mazhukin and I. A. Mikhiliouk -- Ch. 20. Composition Explicit Methods for Stiff Ordinary Differential Equations / Alexei A. Medovikov -- Ch. 21. Numerical Grid - Characteristic Gas dynamic Modeling of the solar wind flow around Comet / Valntina I. Nikolova and Monio D. Kartalev -- Ch. 22. Finite Difference Schemes on Time-Adaptive Meshes for Problems with Generalized Solutions / A. A. Samarskii, B. S. Jovanovic and P. P. Matus / [et al.] -- Ch. 23. Difference Schemes of Second Order of Approximation for Multidimensional Elliptic Equations in Arbitrary Area / A. Samarskii, P. P. Matus and P. N. Vabischevich / [et al.] -- Ch. 24. Grid Approximation of Singularly Perturbed Parabolic Equations, with Convective Terms in the Case of Impermeable Walls / Grigorii I. Shishkin -- Ch. 25. Approximations of the Solution and Diffusion Fluxes for Singularly Perturbed Parabolic Equations with Convective Terms on a Strip / G. I. Shishkin and I. V. Tselishcheva -- Ch. 26. Numerical Implementation of Soil Freezing Models / Vasilii I. Vasiliev, Egor E. Petrov and Vasilii V. Popov -- Ch. 27. Numerical Algorithm for Studying Hydrodynamics in a Glass Melting Furnace / I. Zheleva, V. Kambourova and R. Rusev / [et al.] -- Ch. 28. Numerical Study of Transport and Heat-Transfer Processes in a Glass Melting Furnace / I. Zheleva, V. Kambourova and R. Rusev / [et al.].