4.6 Article

Monotonicity theorem for the uncertain fractional differential equation and application to uncertain financial market

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Summary: The study derives optimal uniform error bounds for the moving least-squares (MLS) mesh-free point collocation method in solving second-order elliptic partial integro-differential equations, and demonstrates improvements in estimate results compared to previous research in elliptic partial differential equations. It also presents optimal convergence rate estimates for second-order elliptic PIDEs and confirms theoretical results through numerical experiments dealing with elliptic PDEs. The study concludes that the MLS collocation scheme is an efficient and reliable numerical method for solving elliptic and parabolic PIDEs in applied areas such as financial engineering.

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