## Numerical Methods for EngineersThis Book Is Intended To Be A Text For Either A First Or A Second Course In Numerical Methods For Students In All Engineering Disciplines. Difficult Concepts, Which Usually Pose Problems To Students Are Explained In Detail And Illustrated With Solved Examples. Enough Elementary Material That Could Be Covered In The First-Level Course Is Included, For Example, Methods For Solving Linear And Nonlinear Algebraic Equations, Interpolation, Differentiation, Integration, And Simple Techniques For Integrating Odes And Pdes (Ordinary And Partial Differential Equations).Advanced Techniques And Concepts That Could Form Part Of A Second-Level Course Includegears Method For Solving Ode-Ivps (Initial Value Problems), Stiffness Of Ode- Ivps, Multiplicity Of Solutions, Convergence Characteristics, The Orthogonal Collocation Method For Solving Ode-Bvps (Boundary Value Problems) And Finite Element Techniques. An Extensive Set Of Graded Problems, Often With Hints, Has Been Included.Some Involve Simple Applications Of The Concepts And Can Be Solved Using A Calculator, While Several Are From Real-Life Situations And Require Writing Computer Programs Or Use Of Library Subroutines. Practice On These Is Expected To Build Up The Reader'S Confidence In Developing Large Computer Codes. |

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A-stable algorithm analytical solution base points bifurcation bifurcation diagrams boundary conditions chemical engineering coefficients computer codes constants convergence corresponding Crank-Nicholson data points defined derivatives described dimensionless discussed easily eigenvalues eigenvectors error estimate evaluated Example 6.1 explicit Euler technique finite difference technique finite elements formula function Gauss elimination Gauss-Seidel technique give grid points implicit IMSL integral internal OC points isothermal TRAM iteration Jacobian Legendre polynomials linear algebraic locations LU Decomp matrix form McGraw Hill multivariable Newton-Raphson method Newton-Raphson technique nonlinear algebraic equations Note obtain OC technique OCFE ODE-IVPs ordinary differential equations orthogonal collocation orthogonal polynomials Pade approximation parameter PDEs problem procedure profiles quadrature reaction reactor residual roots shown in Fig solve successive substitutions Table Taylor series temperature tridiagonal matrix variables vector written York zero