How Long to Read Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations

How Long Does it Take to Read Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations?

It takes the average reader 8 hours and 5 minutes to read Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations by Mitsuhiro T. Nakao

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

Description

In the last decades, various mathematical problems have been solved by computer-assisted proofs, among them the Kepler conjecture, the existence of chaos, the existence of the Lorenz attractor, the famous four-color problem, and more. In many cases, computer-assisted proofs have the remarkable advantage (compared with a “theoretical” proof) of additionally providing accurate quantitative information. The authors have been working more than a quarter century to establish methods for the verified computation of solutions for partial differential equations, mainly for nonlinear elliptic problems of the form -∆u=f(x,u,∇u) with Dirichlet boundary conditions. Here, by “verified computation” is meant a computer-assisted numerical approach for proving the existence of a solution in a close and explicit neighborhood of an approximate solution. The quantitative information provided by these techniques is also significant from the viewpoint of a posteriori error estimates for approximate solutions of the concerned partial differential equations in a mathematically rigorous sense. In this monograph, the authors give a detailed description of the verified computations and computer-assisted proofs for partial differential equations that they developed. In Part I, the methods mainly studied by the authors Nakao and Watanabe are presented. These methods are based on a finite dimensional projection and constructive a priori error estimates for finite element approximations of the Poisson equation. In Part II, the computer-assisted approaches via eigenvalue bounds developed by the author Plum are explained in detail. The main task of this method consists of establishing eigenvalue bounds for the linearization of the corresponding nonlinear problem at the computed approximate solution. Some brief remarks on other approaches are also given in Part III. Each method in Parts I and II is accompanied by appropriate numerical examples that confirm the actual usefulness of the authors’ methods. Also in some examples practical computer algorithms are supplied so that readers can easily implement the verification programs by themselves.

How long is Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations?

Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations by Mitsuhiro T. Nakao is 469 pages long, and a total of 121,471 words.

This makes it 158% the length of the average book. It also has 148% more words than the average book.

How Long Does it Take to Read Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations Aloud?

The average oral reading speed is 183 words per minute. This means it takes 11 hours and 3 minutes to read Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations aloud.

What Reading Level is Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations?

Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations is suitable for students ages 12 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 Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations?

Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations by Mitsuhiro T. Nakao is sold by several retailers and bookshops. However, Read Time works with Amazon to provide an easier way to purchase books.

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