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On the approximate solution of integro-differential equations arising in oscillating magnetic fields. (English) Zbl 1299.34061

In the paper the Volterra integro-differential equation \[ y^{(2)}(t) + a(t)y(t) = g(t) + b(t)\int _0^t \cos (\omega _p s)y(s) ds,\,\,\, y(0) =\alpha , \,\,\, y'(0) = \beta \] is considered where \(a\), \(b\) and \(g\) are given periodic functions of time and \(y\) is an unknown function to be determined. The Shannon wavelets approximation for the numerical solution is proposed. Formal series are derived, their uniform convergence to exact solution is proved and error analysis is performed. Moreover numerical experiments illustrate obtained results.

MSC:

34B05 Linear boundary value problems for ordinary differential equations
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
78A35 Motion of charged particles
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References:

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