Computational Mathematics: Models, Methods, and Analysis by Robert E. White

By Robert E. White

Computational arithmetic: versions, tools, and research with MATLAB® and MPI is a special ebook overlaying the options and strategies on the center of computational technology. the writer offers a hands-on creation to nonlinear, second, and 3D types; nonrectangular domain names; platforms of partial differential equations; and massive algebraic difficulties requiring high-performance computing. The booklet exhibits the best way to observe a version, decide on a numerical procedure, enforce desktop simulations, and investigate the resultant results.

Providing a wealth of MATLAB, Fortran, and C++ code on-line for obtain, the Second Edition of this highly regarded text:

  • Includes a brand new bankruptcy with sections at the finite point procedure, sections on shallow water waves, and sections at the pushed hollow space problem
  • Introduces multiprocessor/multicore desktops, parallel MATLAB, and message passing interface (MPI) within the bankruptcy on high-performance computing
  • Updates and provides code and documentation

Computational arithmetic: versions, tools, and research with MATLAB® and MPI, moment Edition is a perfect textbook for an undergraduate path taught to arithmetic, computing device technological know-how, and engineering scholars. by utilizing code in functional methods, scholars take their first steps towards extra refined numerical modeling.

Show description

Read Online or Download Computational Mathematics: Models, Methods, and Analysis with MATLAB® and MPI, Second Edition (Textbooks in Mathematics) PDF

Best number systems books

Numerical Methods for Elliptic and Parabolic Partial Differential Equations, 1st Edition

This booklet covers numerical tools for partial differential equations: discretization equipment equivalent to finite distinction, finite quantity and finite aspect equipment; answer equipment for linear and nonlinear platforms of equations and grid iteration. The e-book takes account of either the speculation and implementation, supplying concurrently either a rigorous and an inductive presentation of the technical info.

Vibrations of mechanical systems with regular structure (Foundations of Engineering Mechanics)

During this publication, common constructions are de ned as periodic constructions inclusive of repeated components (translational symmetry) in addition to buildings with a geom- ric symmetry. general buildings have for a very long time been attracting the eye of scientists via the extreme great thing about their varieties. they've been studied in lots of components of technology: chemistry, physics, biology, and so forth.

Modular Forms: Basics and Beyond (Springer Monographs in Mathematics)

This is often a complicated publication on modular types. whereas there are lots of books released approximately modular kinds, they're written at an straight forward point, and never so attention-grabbing from the point of view of a reader who already understands the basics. This ebook deals whatever new, that can fulfill the need of any such reader.

Sobolev Gradients and Differential Equations (Lecture Notes in Mathematics)

A Sobolev gradient of a real-valued useful on a Hilbert house is a gradient of that sensible taken relative to an underlying Sobolev norm. This e-book exhibits how descent equipment utilizing such gradients permit remedy of difficulties in differential equations.

Extra info for Computational Mathematics: Models, Methods, and Analysis with MATLAB® and MPI, Second Edition (Textbooks in Mathematics)

Example text

14). 1, f = 0, u(0, t) = sin(2π(0 − vel t)) and u(x, 0) = sin(2πx). It is compared over the time interval t = 0 to t = T = 20 and at x = L = 1 with the exact solution u(x, t) = e−dec t sin(2π(x − vel t)). 2 is proportional to ∆t + ∆x. 15). 15) with k = 1/π 2 , c = 0, f = 0, u(0, t) = 0, u(1, t) = 0 and u(x, 0) = sin(πx). It is compared at (x, t) = (1/2, 1) with the exact solution u(x, t) = e−t sin(πx). 3 is proportional to ∆t + ∆x2 . In order to give an explanation of the discretization errors, one must use higher order Taylor polynomial approximation.

A). 2) and find its solution via the MATLAB command desolve. (b). 4). 4. Consider the time dependent surrounding temperature in problem 3. (a). m to account for the changing surrounding temperature. (b). Experiment with different number of time steps with maxk = 5, 10, 20, 40 and 80. 5. 11) and |bk+1 | ≤ M . 6. 13). 7. 3 to account for the case where the surrounding temperature can depend on time, usur = usur (t). What assumptions should be placed on usur (t) so that the discretization error will be bounded by a constant times the step size?

8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. % This code models heat diffusion in a thin wire. % It executes the explicit finite difference method. 3. DIFFUSION IN A WIRE WITH LITTLE INSULATION 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. ; time(k) = (k-1)*dt; end % % Execute the explicit method using nested loops. 1. 0005 with a time step size equal to 5, then this violates the stability condition so that the model fails. 0005 the model did not fail with a final time equal to 400 and 100 time steps so that the time step size equaled to 4.

Download PDF sample

Rated 4.71 of 5 – based on 48 votes