Equations of Mathematical Physics, Computational Mathematics, and Cubature Formulas by Gennadii Demidenko, Vladimir Vaskevich
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Equations of Mathematical Physics, Computational Mathematics, and Cubature Formulas by
Gennadii Demidenko, Vladimir Vaskevich Sobolev Institute of Mathematics, Novosibirsk, Russia.
The topics covered in this volume include Sobolev’s fundamental works on equations of mathematical physics, computational mathematics, and cubature formulas. Some of the articles are generally unknown to mathematicians because they were published in journals that are difficult to access. This is the first appearance in English of many works by this important Russian mathematician.
Equations of Mathematical Physics, Computational Mathematics, and Cubature Formulas by
Gennadii Demidenko, Vladimir Vaskevich
cover the following topics.
Preface
Academician S. L. Sobolev is a Founder of New Directions of Functional Analysis Yu. G. Reshetnyak
Part I Equations of Mathematical Physics
1. Application of the Theory of Plane Waves to the Lamb Problem by S. L. Sobolev
2. On a New Method in the Plane Problem on Elastic Vibrations by V. I. Smirnov, S. L. Sobolev
3. On Application of a New Method to Study Elastic Vibrations in a Space with Axial Symmetry by V. I. Smirnov, S. L. Sobolev
4. On Vibrations of a Half-Plane and a Layer with Arbitrary Initial Conditions by S. L. Sobolev
5. On a New Method of Solving Problems about Propagation of Vibrations by S. L. Sobolev
6. Functionally Invariant Solutions of the Wave Equation by S. L. Sobolev
7. General Theory of Diffraction of Waves on Riemann Surfaces by S. L. Sobolev
8. The Problem of Propagation of a Plastic State by S. L. Sobolev
9. On a New Problem of Mathematical Physics by S. L. Sobolev
10. On Motion of a Symmetric Top with a Cavity Filled with Fluid by S. L. Sobolev
11. On a Class of Problems of Mathematical Physics by S. L. Sobolev
Part II Computational Mathematics and Cubature Formulas
1. Schwarz’s Algorithm in Elasticity Theory by S. L. Sobolev
2. On Solution Uniqueness of Difference Equations of Elliptic Type by S. L. Sobolev
3. On One Difference Equation by S. L. Sobolev
4. Certain Comments on the Numeric Solutions of Integral Equations by S. L. Sobolev
5. Certain Modern Questions of Computational Mathematics by S. L. Sobolev
6. Functional Analysis and Computational Mathematics by L. V. Kantorovich, L. A. Lyusternik, S. L. Sobolev
7. Formulas of Mechanical Cubatures in n-Dimensional Space by S. L. Sobolev
8. On Interpolation of Functions of n Variables by S. L. Sobolev
9. Various Types of Convergence of Cubature and Quadrature Formulas by S. L. Sobolev
10. Cubature Formulas on the Sphere Invariant under Finite Groups of Rotations by S. L. Sobolev
11. The Number of Nodes in Cubature Formulas on the Sphere by S. L. Sobolev
12. Certain Questions of the Theory of Cubature Formulas by S. L. Sobolev
13. A Method for Calculating the Coefficients in Mechanical Cubature Formulas by S. L. Sobolev
14. On the Rate of Convergence of Cubature Formulas by S. L. Sobolev
15. Theory of Cubature Formulas by S. L. Sobolev
16. Convergence of Approximate Integration Formulas for Functions from L(m)2 by S. L. Sobolev
17. Evaluation of Integrals of Infinitely Differentiable Functions by S. L. Sobolev
18. Cubature Formulas with Regular Boundary Layer by S. L. Sobolev
19. A Difference Analogue of the Polyharmonic Equation by S. L. Sobolev
20. Optimal Mechanical Cubature Formulas with Nodes on a Regular Lattice by S. L. Sobolev
21. Constructing Cubature Formulas with Regular Boundary Layer by S. L. Sobolev
22. Convergence of Cubature Formulas on Infinitely Differentiable Functions by S. L. Sobolev
23. Convergence of Cubature Formulas on the Elements of L (m)2 by S. L. Sobolev
24. The Coefficients of Optimal Quadrature Formulas by S. L. Sobolev
25. On the Roots of Euler Polynomials by S. L. Sobolev
26. On the End Roots of Euler Polynomials by S. L. Sobolev
27. On the Asymptotics of the Roots of the Euler Polynomials by S. L. Sobolev
28. More on the Zeros of Euler Polynomials by S. L. Sobolev
29. On the Algebraic Order of Exactness of Formulas of Approximate Integration by S. L. Sobolev
Index
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