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Green’s Functions
| Content Provider | Scilit |
|---|---|
| Author | Kythe, Prem K. Schäferkotter, Michael R. Puri, Pratap |
| Copyright Year | 2018 |
| Description | A Green's function for a partial differential equation is the solution of its adjoint equation, where the forcing term is the Dirac delta function due to a unit point source in a given domain Ω. This solution enables us to generate solutions of partial differential equations subject to a range of boundary conditions and internal sources. This technique is important in a variety of physical problems. For the derivation of Green's functions, we can assume the presence of an internal source or a certain boundary condition which results in the same effect as the point source. If L is a linear differential operator, andLu(x) = f(x) is a linear differential equation, where x denotes a point in the domain Ω ∈ Rn, and f(x) is the nonhomogeneous term in the differential equation, then the solution of this equation subject to homogeneous boundary conditions can be written in the form u(x) = ∫ · · ·∫ Ω G(x,y) f(y) dy, where G(x,y) is the Green's function, which depends only on the adjoint operator L∗ of L and on the geometry of the problem for homogeneous adjoint initial and boundary conditions. Book Name: Partial Differential Equations and Mathematica |
| Related Links | https://content.taylorfrancis.com/books/download?dac=C2006-0-15865-7&isbn=9781315273105&doi=10.1201/9781315273105-13&format=pdf |
| Ending Page | 276 |
| Page Count | 48 |
| Starting Page | 229 |
| DOI | 10.1201/9781315273105-13 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 2018-10-03 |
| Access Restriction | Open |
| Subject Keyword | Book Name: Partial Differential Equations and Mathematica Mathematical Physics Function Boundary Differential Equation Partial Adjoint Solution of This Equation |
| Content Type | Text |
| Resource Type | Chapter |
