## Computational Mathematics: Models, Methods, and Analysis with MATLAB and MPIComputational Mathematics: Models, Methods, and Analysis with MATLAB and MPI explores and illustrates this process. Each section of the first six chapters is motivated by a specific application. The author applies a model, selects a numerical method, implements computer simulations, and assesses the ensuing results. These chapters include an abundance of MATLAB code. By studying the code instead of using it as a "black box, " you take the first step toward more sophisticated numerical modeling. The last four chapters focus on multiprocessing algorithms implemented using message passing interface (MPI). These chapters include Fortran 9x codes that illustrate the basic MPI subroutines and revisit the applications of the previous chapters from a parallel implementation perspective. All of the codes are available for download from www4.ncsu.edu./~white. This book is not just about math, not just about computing, and not just about applications, but about all three--in other words, computational science. Whether used as an undergraduate textbook, for self-study, or for reference, it builds the foundation you need to make numerical modeling and simulation integral parts of your investigational toolbox. |

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An exceptional book , with lucid explanations of applied mathematics . The author's knowledge in applied computational programming is excellent . The Kryolov methods given the last chapter was helpful for developing a 3D code in my master thesis in computation of fluid flow. The MPI programs are worth trying and gives deep insights to High performance computing /Parallel Programming.

### Contents

xv | |

1 | |

Chapter 2 Steady State Discrete Models | 51 |

Chapter 3 Poisson Equation Models | 99 |

Chapter 4 Nonlinear and 3D Models | 145 |

Chapter 5 Epidemics Images and Money | 189 |

Chapter 6 High Performance Computing | 237 |

### Other editions - View all

Computational Mathematics: Models, Methods, and Analysis with MATLAB and MPI Robert E. White No preview available - 2003 |

### Common terms and phrases

algebraic system algorithm American put option approximation array block boundary conditions coeﬃcient column vector components computations conjugate gradient method Consider continuous model cooling ﬁn deﬁned derivative diagonal direction discrete model domain decomposition dot products eﬀects endloop error example executed experiment with diﬀerent Figure ﬁnd ﬁnite diﬀerence method ﬁrst ﬁxed ﬂoating point ﬂow ﬂuid Fortran function Gaussian elimination GMRES grid row heat diﬀusion ierr initial guess integer inverse iterative methods linear loc_a loc_b loc_dot loc_n MATLAB code matrix products maxk mpi_comm_world,ierr mpi_reduce MPI/Fortran my_rank my_rank.eq.0 nodes nonlinear number of processors partial diﬀerential equation payoﬀ Picard Picard iteration Poisson problem pollutant positive deﬁnite preconditioner print*,'my_rank my_rank problem put option contract rank Schur complement solution speedup SSOR preconditioner stability condition steady steepest descent subroutine Theorem tridiagonal matrix uk+1 underlying asset unknowns upper triangular utemp velocity wire xm+1 zero