Numerical solution of uncertain partial differential equations and its applications

Lu Yang () and Yang Liu ()
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Lu Yang: Xi’an University of Finance and Economics
Yang Liu: Beihang University

Fuzzy Optimization and Decision Making, 2025, vol. 24, issue 1, No 3, 69-98

Abstract: Abstract Uncertain partial differential equations are widely used in practice, such as demography, traffic flows and so on. This paper proves an existence and uniqueness theorem for a class of uncertain partial differential equations. Then the properties of $$\alpha$$ α -path are given based on linear growth, Lipschitz and regular conditions. Since uncertain partial differential equations are difficult to get analytical solutions, this paper presents a formula which combines an uncertain partial differential equation with a class of classical partial differential equations. Based on the formula, an algorithm for calculating the inverse uncertainty distribution of solution of an uncertain partial differential equation is also deduced. Finally, expected value, extreme value, first hitting time, time and spatial integrals of the solution of uncertain partial differential equation are also discussed.

Keywords: Uncertainty theory; Uncertain partial differential equation; Existence and uniqueness theorem; Numerical solution (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10700-025-09439-z

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