The Method of Fractional Steps

1. Front Matter

   Pages I-VIII

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2. Uniform Schemes

   • N. N. Yanenko

   Pages 1-16

3. Simple Schemes in Fractional Steps for the Integration of Parabolic Equations

   • N. N. Yanenko

   Pages 17-41

4. Application of the Method of Fractional Steps to Hyperbolic Equations

   • N. N. Yanenko

   Pages 42-53

5. Application of the Method of Fractional Steps to Boundary Value Problems for Laplace’s and Poisson’s Equations

   • N. N. Yanenko

   Pages 54-81

6. Boundary Value Problems in the Theory of Elasticity

   • N. N. Yanenko

   Pages 82-91

7. Schemes of Higher Accuracy

   • N. N. Yanenko

   Pages 92-98

8. Integro-differential, Integral, and Algebraic Equations

   • N. N. Yanenko

   Pages 99-101

9. Some Problems of Hydrodynamics

   • N. N. Yanenko

   Pages 102-116

10. General Definitions

    • N. N. Yanenko

    Pages 117-131

11. The Method of Weak Approximation and the Construction of the Solution of the Cauchy Problem in Banach Space

    • N. N. Yanenko

    Pages 132-150

12. Back Matter

    Pages 151-160

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The method of. fractional steps, known familiarly as the method oi splitting, is a remarkable technique, developed by N. N. Yanenko and his collaborators, for solving problems in theoretical mechanics numerically. It is applicable especially to potential problems, problems of elasticity and problems of fluid dynamics. Most of the applications at the present time have been to incompressible flow with free bound­ aries and to viscous flow at low speeds. The method offers a powerful means of solving the Navier-Stokes equations and the results produced so far cover a range of Reynolds numbers far greater than that attained in earlier methods. Further development of the method should lead to complete numerical solutions of many of the boundary layer and wake problems which at present defy satisfactory treatment. As noted by the author very few applications of the method have yet been made to problems in solid mechanics and prospects for answers both in this field and other areas such as heat transfer are encouraging. As the method is perfected it is likely to supplant traditional relaxation methods and finite element methods, especially with the increase in capability of large scale computers. The literal translation was carried out by T. Cheron with financial support of the Northrop Corporation. The editing of the translation was undertaken in collaboration with N. N. Yanenko and it is a plea­ sure to acknowledge his patient help and advice in this project. The edited manuscript was typed, for the most part, by Mrs.

• Mathematische Physik
• Potential
• Variables
• finite element method
• mathematical physics

• University of California, Berkeley, USA

  Maurice Holt

• Siberian Branch Computing Center, U.S.S.R. Academy of Sciences, Novosibirsk, USSR

  N. N. Yanenko

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