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 a₁ a₂ algorithm analytical solution Ax)² b₁ b₂ base points bifurcation bifurcation diagrams boundary conditions chemical engineering coefficients constants convergence data points defined degree polynomial derivatives described dimensionless discussed easily eigenvalues eigenvectors error estimate evaluated Example explicit Euler technique finite difference finite element formula forward difference function Gauss elimination give given grid points h₁ h₂ implicit IMSL integration iteration Jacobian k₁ k₂ Legendre polynomials linear locations McGraw Hill multivariable Newton-Raphson technique Newton's nonlinear algebraic equations Note obtain OC points ODE-IVPs ordinary differential equations Padé approximation parameter PDEs Prob problem R₁ R₂ reactor RK technique roots solve stability envelopes successive substitutions symmetric matrix Taylor series temperature tridiagonal matrix values variables vector written x₁ y₁ y₂ yn+1 York zero дх