Journal of Mathematical Analysis and Applications· 2026Q1
Stability and numerical solutions of nonlinear implicit stochastic differential equations
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- Q1SCImago
- 2026year
Short summary
New sufficient conditions for solvability and stochastic asymptotic stability are established for nonlinear time-varying stochastic differential-algebraic equations (SDAEs), with the explicit Euler method proven to converge.
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Key points
- Established sufficient conditions for solvability and stochastic asymptotic stability in nonlinear time-varying SDAEs.
- Proved convergence of the explicit Euler method for these equations as mesh size approaches zero.
- Demonstrated that solvability conditions are necessary for linear time-varying SDAEs.
- Presented examples to validate the theoretical results.
AI-generated from the title and abstract; the full text is not read.
Abstract
This paper investigates the solvability, stability, and convergence of numerical solutions for nonlinear stochastic differential-algebraic equations (SDAEs) with time-varying coefficients. We establish sufficient conditions for solvability and stochastic asymptotic stability, and prove that the explicit Euler method converges as the mesh size tends to zero. Moreover, we show that the solvability conditions are also necessary in the linear case. Several examples are presented to illustrate the theoretical results. To the best of our knowledge, these results are new for time-varying SDAEs.
The authors' abstract, as published at the source. Journal of Mathematical Analysis and Applications, 2026 · DOI ↗
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Field: Numerical Analysis
Numerical AnalysisMathematics