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By Yogesh Jaluria

IntroductionIntroductory RemarksNumerical SolutionsImportance of Analytical ResultsPhysical ConsiderationsApplication of machine the way to Engineering ProblemsOutline and Scope of the BookBasic concerns in desktop MethodsIntroductionComputational ProcedureNumerical mistakes and AccuracyIterative ConvergenceNumerical ParametersA evaluation of MATLAB ProgrammingIntroductionMATLAB EnvironmentOrdinary Differential Read more...

summary: IntroductionIntroductory RemarksNumerical SolutionsImportance of Analytical ResultsPhysical ConsiderationsApplication of desktop how to Engineering ProblemsOutline and Scope of the BookBasic issues in desktop MethodsIntroductionComputational ProcedureNumerical blunders and AccuracyIterative ConvergenceNumerical ParametersA evaluation of MATLAB ProgrammingIntroductionMATLAB EnvironmentOrdinary Differential EquationsInput/OutputScript m-FilesFunction m-FilesPlottingTaylor sequence and Numerical DifferentiationIntroductionThe Taylor SeriesDirect Approximation of DerivativesTaylor-Series App

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Additional info for Computer Methods for Engineering with MATLAB® Applications, Second Edition

Example text

These include Basic, Pascal, C, Lisp, and others. Among these, Basic, which stands for beginner’s all-purpose symbolic instruction code, was also a widely used language, particularly on PCs, since it is generally simpler to use than Fortran and is well suited for small programs. However, it is not as versatile as Fortran and is often inconvenient for large, ­complex programs. Many improved versions of Basic have been developed in recent years, and many of the constraints that existed in the earlier versions have been eliminated.

In numerical methods based on iteration, a convergence criterion ε is employed to decide when to terminate the iteration. Generally, the convergence criterion is applied to a physical variable in the problem, and computation is stopped when the change from one iteration to the next is less than the chosen value of ε. A relationship between ε and the accuracy of the numerical results may be obtained by a comparison of the computed values with the analytical solution that may be available for a simplified circumstance.

1 Method Selection Frequently, several methods are available for the numerical solution of a given ­mathematical problem. The selection of the method to be employed, from among the several applicable methods, is an important consideration and is generally based on many relevant criteria, such as the following: 1. Previous experience with a given method 24 Computer Methods for Engineering with MATLAB ® Applications The accuracy of a given method is an important consideration in its selection for solving a particular problem.

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