On the modified Newton's approximation method for the solution of nonlinear singular integral equations (Q1977497)
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scientific article; zbMATH DE number 1448529
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the modified Newton's approximation method for the solution of nonlinear singular integral equations |
scientific article; zbMATH DE number 1448529 |
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On the modified Newton's approximation method for the solution of nonlinear singular integral equations (English)
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22 November 2000
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The modified Newton method \[ x_{n+1}=x_n-[K'(x_0)]K(x_n), \quad n=1,2,\ldots, \] for the nonlinear singular integral equation \[ Kx \equiv F(t,x(t))-B\left(\frac{1}{\pi}\int_a^b\frac{G(\tau, x(\tau))}{\tau-t} dt\right)=0 \] is investigated. Here \(K'(x_0)\) is Fréchet differentiable, \(F,B,G\) are nonlinear functions.
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modified Newton method
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nonlinear singular integral equation
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