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The boundary-element method for the determination of a heat source dependent on one variable
This paper investigates the inverse problem of determining a heat source in the parabolic heat equation using the usual conditions of the direct problem and a supplementary condition, called anExpand
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The Cauchy problem for Laplace’s equation via the conjugate gradient method
A variational formulation of the Cauchy problem for the Laplace equation is studied. An efficient conjugate gradient method based on an optimal-order stopping criterion is presented together with itsExpand
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A non-local boundary value problem method for the Cauchy problem for elliptic equations
Let H be a Hilbert space with norm || ||, A:D(A) ⊂ H → H a positive definite, self-adjoint operator with compact inverse on H, and T and given positive numbers. The ill-posed Cauchy problem forExpand
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An efficient method for computing eigenelements of Sturm-Liouville fourth-order boundary value problems
TLDR
An efficient method based on the Adomian decomposition for computing eigenelements of fourth-order Sturm-Liouville boundary value problems is developed. Expand
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Free convection boundary-layer flow along a vertical surface in a porous medium with Newtonian heating
Abstract In this paper the steady free convection boundary-layer flow along a vertical surface embedded in a porous medium with Newtonian heating is investigated. The mathematical problem reduces toExpand
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The Decomposition Approach to Inverse Heat Conduction
Adomian's decomposition approach is employed for solving some inverse boundary value problems in heat conduction. Further, the mollification method is applied to deal with noisy input data and obtainExpand
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The method of fundamental solutions for nonlinear functionally graded materials
In this paper, we investigate the application of the method of fundamental solutions (MFS) to two-dimensional steady-state heat conduction problems for both isotropic and anisotropic, single andExpand
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Determination of a spacewise dependent heat source
This paper investigates the inverse problem of determining a spacewise dependent heat source in the parabolic heat equation using the usual conditions of the direct problem and information from aExpand
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A survey of applications of the MFS to inverse problems
The method of fundamental solutions (MFS) is a relatively new method for the numerical solution of boundary value problems and initial/boundary value problems governed by certain partial differentialExpand
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Application of the boundary element method to inverse heat conduction problems
Abstract The solution of the one-dimensional, linear, inverse, unsteady heat conduction problem (IHCP) in a slab geometry is analysed. The initial temperature is known, together with a condition onExpand
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