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By Yogesh Jaluria

IntroductionIntroductory RemarksNumerical SolutionsImportance of Analytical ResultsPhysical ConsiderationsApplication of laptop the right way to Engineering ProblemsOutline and Scope of the BookBasic concerns in desktop MethodsIntroductionComputational ProcedureNumerical error 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 machine MethodsIntroductionComputational ProcedureNumerical mistakes and AccuracyIterative ConvergenceNumerical ParametersA overview 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 resources for Computer Methods for Engineering with MATLAB® Applications, Second Edition

Example text

In the solution of parabolic PDEs, for instance, the explicit schemes, which are generally simpler to use, often restrict the step size to small values, making these schemes inefficient. Then the implicit methods, which usually do not have such constraints resulting from stability considerations, are ­preferred. Thus, the numerical instability of the method is an important ­consideration in its selection. As listed before, several other considerations also play an important role in the selection of the method.

5. Check if the convergence criterion SN/S < ε is satisfied. 6. If the convergence criterion is satisfied, stop and print the results on n, S, and E. 7. If the convergence criterion is not satisfied, advance n by 1 and go back to step 4. 8. Continue till convergence criterion is satisfied or a given maximum value of n is reached. 2 in Fortran 77. This program is presented to show the logic and the various steps involved and for those who are familiar with the language. The program would then yield the number of terms needed for the ­preceding convergence criterion to be satisfied, the computed sum S of the series, and the percentage error E.

However, it is very slow in the execution of the program. A compiler, on the other hand, organizes the entire program into a set of machine instructions and locations, and several compilers are available. The compiler is often written for a given ­computer system and is generally a completely separate process undertaken before the program is run. Once the machine code has been produced by the compiler, the compiled ­program is stored and the program may be executed with a separate ­command. A single command that compiles and executes the program may also be used.

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