## Computational Mathematics in Engineering and Applied Science: ODEs, DAEs, and PDEsComputational Mathematics in Engineering and Applied Science provides numerical algorithms and associated software for solving a spectrum of problems in ordinary differential equations (ODEs), differential algebraic equations (DAEs), and partial differential equations (PDEs) that occur in science and engineering. It presents detailed examples, each including a complete analysis of a computer code written in transportable Fortran 77. Each example also includes a discussion of the problem equations, the coding of the equations, and the computed numerical solution. The benefits of using quality general-purpose library routines to solve ODE/DAE/PDE problems are illustrated as well. This popular, classic book is a valuable reference for methodologies in numerical mathematics applicable to a broad spectrum of problems encountered across many disciplines- virtually all fields of science and engineering. It also serves as an excellent text for senior undergraduates or beginning graduate students in computational science. |

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### Contents

The General Problems in Ordinary Differential Algebraic | 1 |

The Numerical Integration of Initial Value Ordinary Differential Equations | 17 |

Partial Differential Equations First Order in Time | 195 |

Partial Differential Equations First Order in Time continued | 279 |

Partial Differential Equations Second and Zeroth Order in Time | 475 |

### Common terms and phrases

analytical solution array boundary conditions coefficients COMMON/T DASSL data file defined dependent variable DERIVATIVE ROW DERV1 DERV2 DIFF(X.T DIFFERENTIAL EQUATIONS Dirichlet boundary conditions DOUBLE PRECISION A-H.O-Z eigenvalues END OF RUNS equa equations 3.11 error tolerance Euler method EXACT SOLUTION finite difference finite element first-order following points fourth-order function grid points IMPLICIT DOUBLE PRECISION initial condition initial value INTEGRATION ALGORITHM integration step Jacobian matrix KUTTA linear lines solution listed in Program loop LSODE main program MAXIMUM INTEGRATION ERROR method of lines Neumann boundary conditions nonlinear NORUN note the following NSTOP NUMBER OF DIFFERENTIAL numerical and analytical numerical integration numerical solution ODE integrator ODE problem ODE system One-dimensional Output from Programs parabolic PARAMETER PARTIAL DERIVATIVE PDEs PRINT THE NUMERICAL RETURN END Program RETURN END SUBROUTINE Runge-Kutta method second-order SNSQE solution of equation spatial grid SPLINE SUBROUTINE DERV Subroutine INITAL Subroutine PRINT Table Taylor series temporal derivatives tion