Computational mathematics: Models, methods, and analysis by Robert E. White PDF

By Robert E. White

ISBN-10: 0203494474

ISBN-13: 9780203494479

ISBN-10: 1584883642

ISBN-13: 9781584883647

This textbook is written basically for undergraduate mathematicians and in addition appeals to scholars operating at a sophisticated point in different disciplines. The textual content starts off with a transparent motivation for the research of numerical research in keeping with real-world difficulties. The authors then increase the required equipment together with new release, interpolation, boundary-value difficulties and finite parts. all through, the authors regulate the analytical foundation for the paintings and upload old notes at the improvement of the topic. there are various workouts for college students "This publication isn't just approximately math, not only approximately computing, and never almost about purposes, yet approximately all 3 - in different phrases, computational technology. no matter if used as an undergraduate textbook, for self-study, or for reference, it builds the basis you must make numerical modeling and simulation indispensable components of your investigational toolbox."--BOOK JACKET. 1 Discrete Time-Space types 1 -- 1.1 Newton Cooling versions 1 -- 1.2 warmth Diffusion in a cord nine -- 1.3 Diffusion in a twine with Little Insulation 17 -- 1.4 circulate and rot of a Pollutant in a circulate 25 -- 1.5 warmth and Mass move in instructions 32 -- 1.6 Convergence research forty two -- 2 regular nation Discrete versions fifty one -- 2.1 regular country and Triangular Solves fifty one -- 2.2 warmth Diffusion and Gauss removal fifty nine -- 2.3 Cooling Fin and Tridiagonal Matrices sixty eight -- 2.4 Schur supplement seventy seven -- 2.5 Convergence to regular nation 86 -- 2.6 Convergence to non-stop version ninety one -- three Poisson Equation versions ninety nine -- 3.1 regular kingdom and Iterative equipment ninety nine -- 3.2 warmth move in second Fin and SOR 107 -- 3.3 Fluid move in a 2nd Porous Medium 116 -- 3.4 perfect Fluid move 122 -- 3.5 Deformed Membrane and Steepest Descent a hundred thirty -- 3.6 Conjugate Gradient technique 138 -- four Nonlinear and 3D versions a hundred forty five -- 4.1 Nonlinear difficulties in a single Variable a hundred forty five -- 4.2 Nonlinear warmth move in a twine 152 -- 4.3 Nonlinear warmth move in second 159 -- 4.4 regular nation 3D warmth Diffusion 166 -- 4.5 Time based 3D Diffusion 171 -- 4.6 excessive functionality Computations in 3D 179 -- five Epidemics, photographs and cash 189 -- 5.1 Epidemics and Dispersion 189 -- 5.2 Epidemic Dispersion in second 197 -- 5.3 photo recovery 204 -- 5.4 recovery in second 213 -- 5.5 alternative agreement types 219 -- 5.6 Black-Scholes version for 2 resources 228 -- 6 excessive functionality Computing 237 -- 6.1 Vector desktops and Matrix items 237 -- 6.2 Vector Computations for warmth Diffusion 244 -- 6.3 Multiprocessors and Mass move 249 -- 6.4 MPI and the IBM/SP 258 -- 6.5 MPI and Matrix items 263 -- 6.6 MPI and second versions 268 -- 7 Message Passing Interface 275 -- 7.1 simple MPI Subroutines 275 -- 7.2 lessen and Broadcast 282 -- 7.3 assemble and Scatter 288 -- 7.4 Grouped facts kinds 294 -- 7.5 Communicators 301 -- 7.6 Fox set of rules for AB 307 -- eight Classical tools for Ax = d 313 -- 8.1 Gauss removal 313 -- 8.2 Symmetric optimistic convinced Matrices 318 -- 8.3 area Decomposition and MPI 324 -- 8.4 SOR and P-regular Splittings 328 -- 8.5 SOR and MPI 333 -- 8.6 Parallel ADI Schemes 339 -- nine Krylov equipment for Ax = d 345 -- 9.1 Conjugate Gradient approach 345 -- 9.2 Preconditioners 350 -- 9.3 PCG and MPI 356 -- 9.4 Least Squares 360 -- 9.5 GMRES 365 -- 9.6 GMRES(m) and MPI 372

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2004 by Chapman & Hall/CRC 38 CHAPTER 1. m 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. % The is pollutant flow across a lake. % The explicit finite difference method is used. 1; %decay rate % Set initial conditions. 5. HEAT AND MASS TRANSFER IN TWO DIRECTIONS 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 39 end % Set upwind boundary conditions. 1; end end % % Execute the explicit finite difference method. m. 5 is sequence of mesh plots for the concentrations at various time steps.

25. 05 and n = 5, 10, 20, respectively. 3. 1. 25 and maxk = 30, 60 and 120, respectively. 4. 0005. Be sure to adjust the time step so that the stability condition holds. 5. Consider the variation on the thin wire where heat is lost through the surface of the wire. m and experiment with the C and r parameters. Explain your computed results. 6. Consider the variation on the thin wire where heat is generated by f = 1 + sin(π10t). m and experiment with the parameters. 7. 1). Compute Ak for k = 10, 100, 1000 for different values of alpha so that the stability condition either does or does not hold.

8. m experiment with different time mesh sizes, maxk = 100, 200, 400. Be sure to consider the stability constraint. 9. m experiment with different space mesh sizes, nx = 5, 10 and 20. Be sure to consider the stability constraint. 10. 04. Be sure to make any adjustments to the time step so that the stability condition holds. 11. m. © 2004 by Chapman & Hall/CRC 42 CHAPTER 1. DISCRETE TIME-SPACE MODELS (a). Adjust the magnitudes of the velocity components and observe stability as a function of wind velocity.

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Computational mathematics: Models, methods, and analysis with MATLAB and MPI by Robert E. White


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