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Keywords
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Black–Scholes equation, Domain decomposition method, Spectral collocation technique, Predictor–corrector method, Option pricing
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Abstract
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In this work, we use the spectral collocation technique for spatial derivatives and predictor–corrector method for time integration to solve the Black–Scholes (B–S) equation. If the spectral collocation method is worked properly, then we get high accuracy in the numerical solutions. Firstly, theory of application of Chebyshev spectral collocation technique and domain decomposition method on the B–S equation is presented. This method gets a stiff system of differential equations. Secondly, by using the predictor–corrector method with variable step size, we obtain the high accuracy approximate solution in the numerical integration of the stiff system of DEs. We present the order of accuracy for the proposed method. The numerical results show the efficiency and validity of the method.
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