Computer Methods for Engineering with MATLAB® Applications, by Yogesh Jaluria

By Yogesh Jaluria

IntroductionIntroductory RemarksNumerical SolutionsImportance of Analytical ResultsPhysical ConsiderationsApplication of laptop ways to Engineering ProblemsOutline and Scope of the BookBasic concerns in laptop MethodsIntroductionComputational ProcedureNumerical blunders and AccuracyIterative ConvergenceNumerical ParametersA evaluate of MATLAB ProgrammingIntroductionMATLAB EnvironmentOrdinary Differential Read more...

summary: IntroductionIntroductory RemarksNumerical SolutionsImportance of Analytical ResultsPhysical ConsiderationsApplication of computing device easy methods to Engineering ProblemsOutline and Scope of the BookBasic issues in machine MethodsIntroductionComputational ProcedureNumerical mistakes 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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The computer storage requirements of the method are generally important in the simulation of large systems that are of interest in engineering applications. For Basic Considerations in Computer Methods 25 example, the Jacobi method for solving a system of linear algebraic equations involves the storage of the matrices of the unknowns at two iterative steps, the ­present and the previous one, whereas the Gauss–Seidel method requires the storage of only the latest values. Thus, the latter method requires only about half the storage needed by the first method.

This series represents the ­binomial expansion of 1/(1 − x), which therefore gives the exact value SX of the series. Compare the exact and computed values of S to determine the numerical error. Discuss the dependence of the sum S on the number of terms n taken in the series. 1 are to be added sequentially. The basic considerations relevant to convergence are discussed in detail later in this chapter. 1, is larger than the next term, for |x| < 1. Thus, the contribution of each additional term to the sum decreases as n is increased.

The consideration of numerical errors and the accuracy of the results is important in the numerical solution of any given problem. The various types of errors that arise in the computational approach are discussed, along with methods that may be employed for reducing the error. The accuracy of the solution may often be estimated by comparing the numerical results with those from the analytical solution for simpler problems, since the analytical solution of the given problem is presumably not available.

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