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Demonstrates numerical solutions of the generalized Black-Scholes equation, indicating improved stability and performance.
This article presents the use of differential quadrature method based on modified cubic B-splines for obtaining the numerical solution of generalized Black-Scholes equation. The generalized Black-Scholes equation is transformed to a time progressing non-degenerate equation by logarithmic transformation and the transformed setup is spatially discretized using differential quadrature method. The time integration of the corresponding ODE system is executed with SSPRK54 and generalized trapezoidal formula (GTF). Several test problems are examined for the validation of theoretical results. The numerical experiments are compared and computational stability of the system is also ensured.
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Nizamudheen et al. (2026) studied this question.
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