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Numerical solution of uncertain partial differential equations and its applications

Author

Listed:
  • Lu Yang

    (Xi’an University of Finance and Economics)

  • Yang Liu

    (Beihang University)

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.

Suggested Citation

  • Lu Yang & Yang Liu, 2025. "Numerical solution of uncertain partial differential equations and its applications," Fuzzy Optimization and Decision Making, Springer, vol. 24(1), pages 69-98, March.
    • Handle: RePEc:spr:fuzodm:v:24:y:2025:i:1:d:10.1007_s10700-025-09439-z
    DOI: 10.1007/s10700-025-09439-z
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