Boundary-value problems (Neumann condition)

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In summary, the conversation is about someone looking for a book that explains von Neumann conditions and contains solved problems related to boundary-value problems in heat transfer or the wave equation. The recommendation given is "PDE with Fourier Series and Boundary Value Problems" by Asmar. The person asking the question also mentions using "Differential Equations with Boundary-Value Problems" by Dennis G. Zill, but is unsure if it covers Neumann Boundary Conditions. They ask for clarification on which problems in Asmar's book have Neumann Boundary Conditions.
  • #1
phioder
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Hello

Looking for basic boundary-value problems with von Neumann conditions, more specific the applied ones to heat transfer or the wave equation.
Could anyone recommend some good book that explains in an easy way the von Neumann conditions or has some solved problems related to the von Neumann conditions?

Best Regards
 
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waht said:
PDE with Fourier Series and Boundary Value Problems by Asmar

Thank you for your reply and information, it seems that the book is what I'm looking for, but I have some questions before ordering (~$100 USD).

As for now I have being using Dennis G. Zill, Differential Equations with Boundary-Value Problems with a very good but quick introduction to Partial Differential Equations in Cylindrical and Polar coordinates, Bessel Functions, basic and general Dirichlet problems.

Does the book by Asmar approaches problems with Neumann Boundary Conditions (Chapter 5.4?) or the problems presented on his book are defined only with Dirichlet conditions?

If there are some problems with Neumann Boundary Conditions , could you tell me which ones? Sorry about the question but the library doesn't have the book and the table of contents at Amazon tells me that the book presents only very basic problems with general Dirichlet boundary conditions.

Best Regards
 

What is a boundary-value problem?

A boundary-value problem is a type of mathematical problem that involves finding a solution to a differential equation subject to certain boundary conditions. These conditions are specified at the boundaries of the domain in which the equation is defined.

What is the Neumann condition?

The Neumann condition is a type of boundary condition that specifies the value of the derivative of the solution at the boundary of a domain. It is named after German mathematician Carl Neumann.

When are Neumann conditions used?

Neumann conditions are used when the physical problem being modeled requires the specification of the flux or flow of a quantity at the boundary. This can include heat, mass, or momentum transfer.

How are Neumann conditions applied in numerical methods?

In numerical methods, Neumann conditions are typically approximated by finite difference or finite element methods, where the derivative of the solution at the boundary is approximated using neighboring points in the discretized domain.

What are some examples of boundary-value problems with Neumann conditions?

Examples of boundary-value problems with Neumann conditions include the heat conduction equation with insulation on one side, the diffusion equation with a specified concentration at the boundary, and the fluid flow equation with a no-slip condition at the boundary.

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