Titlebook: Difference Methods and Their Extrapolations; G. I. Marchuk,V. V. Shaidurov Book 1983 Springer-Verlag New York Inc. 1983 Algebra.Differenti

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General Properties,ccurate approximate solution using the Richardson extrapolation with higher-order differences. We then extend these results to abstract problems: we first, formulate a sufficient condition for the existence of an expansion of the approximate solution in powers of the difference net mesh-size; then w

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First-Order Ordinary Differential Equations,the mesh-size of the net on which the reduction of the differential equation to a difference equation is carried out. At present many methods exist for finding approximate solutions with a given degree of accuracy when the solution of the differential equation is smooth. The Runge-Kutta method is on

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The One-Dimensional Stationary Diffusion Equation,y of nuclear reactors, where the diffusion approximation of the transport equation is of great importance. In ecology the computation of the diffusion of industrial aerosols is of great importance. Important diffusion problems occur in physics, chemistry, geophysics, and other fields of science. Bec

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Book 1983before, create new demands on applied mathematics, and have acted as a major impetus to the development of computer science. For example, when investigating the stability of a fluid flowing around an object one needs to solve the low viscosity form of certain hydrodynamic equations describing the fl

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0172-4568 t provided the resources for computations which make use of methods with low accuracy. The computational speed of computers is continually increasing, while memory still remains a problem when one handles large arrays. More accurate numerical methods allow us to reduce the overall computation time b

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