Galerkin finite element method for one nonlinear integro-differential model (Q716085)
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scientific article; zbMATH DE number 5880126
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Galerkin finite element method for one nonlinear integro-differential model |
scientific article; zbMATH DE number 5880126 |
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Galerkin finite element method for one nonlinear integro-differential model (English)
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19 April 2011
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The authors derive a Galerkin finite element method for the integro-differential equation \[ \partial u(x,t)/ \partial t= \bigg(1 + \int_0^t \int_0^1 \big(\partial u (x,\tau)/\partial x\big)^2\, dx\, d\tau\bigg) \partial^2 u(x,t)/\partial x^2 + f(x,t) \] subject to homogeneous boundary conditions and an arbitrary initial condition. A brief error analysis is provided and numerical examples are given.
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nonlinear integro-differential equations
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initial-boundary value problem
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Galerkin finite element method
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error analysis
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numerical examples
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