How Long to Read Estimating the Error of Numerical Solutions of Systems of Reaction-Diffusion Equations

How Long Does it Take to Read Estimating the Error of Numerical Solutions of Systems of Reaction-Diffusion Equations?

It takes the average reader 2 hours and 7 minutes to read Estimating the Error of Numerical Solutions of Systems of Reaction-Diffusion Equations by Donald J. Estep

Assuming a reading speed of 250 words per minute. Learn more

Description

This paper is concerned with the computational estimation of the error of numerical solutions of potentially degenerate reaction-diffusion equations. The underlying motivation is a desire to compute accurate estimates as opposed to deriving inaccurate analytic upper bounds. In this paper, we outline, analyze, and test an approach to obtain computational error estimates based on the introduction of the residual error of the numerical solution and in which the effects of the accumulation of errors are estimated computationally. We begin by deriving an a posteriori relationship between the error of a numerical solution and its residual error using a variational argument. This leads to the introduction of stability factors, which measure the sensitivity of solutions to various kinds of perturbations. Next, we perform some general analysis on the residual errors and stability factors to determine when they are defined and to bound their size. Then we describe the practical use of the theory to estimate the errors of numerical solutions computationally. Several key issues arise in the implementation that remain unresolved and we present partial results and numerical experiments about these points. We use this approach to estimate the error of numerical solutions of nine standard reaction-diffusion models and make a systematic comparison of the time scale over which accurate numerical solutions can be computed for these problems. We also perform a numerical test of the accuracy and reliability of the computational error estimate using the bistable equation. Finally, we apply the general theory to the class of problems that admit invariant regions for the solutions, which includes seven of the main examples. Under this additional stability assumption, we obtain a convergence result in the form of an upper bound on the error from the a posteriori error estimate. We conclude by discussing the preservation of invariant regions under discretization.

How long is Estimating the Error of Numerical Solutions of Systems of Reaction-Diffusion Equations?

Estimating the Error of Numerical Solutions of Systems of Reaction-Diffusion Equations by Donald J. Estep is 125 pages long, and a total of 31,875 words.

This makes it 42% the length of the average book. It also has 39% more words than the average book.

How Long Does it Take to Read Estimating the Error of Numerical Solutions of Systems of Reaction-Diffusion Equations Aloud?

The average oral reading speed is 183 words per minute. This means it takes 2 hours and 54 minutes to read Estimating the Error of Numerical Solutions of Systems of Reaction-Diffusion Equations aloud.

What Reading Level is Estimating the Error of Numerical Solutions of Systems of Reaction-Diffusion Equations?

Estimating the Error of Numerical Solutions of Systems of Reaction-Diffusion Equations is suitable for students ages 10 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy Estimating the Error of Numerical Solutions of Systems of Reaction-Diffusion Equations?

Estimating the Error of Numerical Solutions of Systems of Reaction-Diffusion Equations by Donald J. Estep is sold by several retailers and bookshops. However, Read Time works with Amazon to provide an easier way to purchase books.

To buy Estimating the Error of Numerical Solutions of Systems of Reaction-Diffusion Equations by Donald J. Estep on Amazon click the button below.