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In this paper, the Black–Scholes equation is solved using a new technique. This scheme is derived by combining the Laplace transform method and the nonstandard finite difference (NSFD) strategy. The qualitative properties of the method are discussed, and it is shown that the new method is positive, stable, and consistent when low volatility is assumed. The efficiency of the new method is demonstrated by a numerical example.
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Khalsaraei et al. (2023) studied this question.
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