To further explore higher-order explicit schemes for SDEs
Research gap analysis derived from 3 mathematics papers in our local library.
The gap
To further explore higher-order explicit schemes for SDEs with non-Lipschitz coefficients.
Evidence profile
Stated in the cells research gap and cells future research sections of the source papers, classified as general, spanning 3 journals.
Research trend
Established — well-defined area with open sub-problems.
Supporting evidence — 5 representative gaps
- Unconditionally positivity-preserving explicit order-one strong approximations of financial SDEs with non-Lipschitz coefficients (2026) · Journal of Computational and Applied Mathematics · doi
Existing numerical methods for SDEs with non-Lipschitz coefficients have limitations. - The Euler-Maruyama method produces divergent results for certain SDEs.
generalstated in cells research gapevidence 5/5Keywords: existing numerical methods sdes non-lipschitz coefficients have limitations - Parameter-Related strong convergence rates of Euler-type methods for time-changed stochastic differential equations (2026) · Numerical Algorithms · doi
The standard Euler–Maruyama method is known to be divergent in general for time-changed SDEs with super-linear growth coefficients. - Existing works using random step sizes typically preserve the classical convergence order of 1/2.
generalstated in cells research gapevidence 5/5Keywords: standard euler maruyama method known divergent general time-changed - Parameter-Related strong convergence rates of Euler-type methods for time-changed stochastic differential equations (2026) · Numerical Algorithms · doi
To further study the properties of time-changed SDEs. - To develop more efficient numerical methods for time-changed SDEs. - To apply the results to real-world problems in various scientific disciplines.
generalstated in cells future researchevidence 5/5Keywords: further study properties time-changed sdes develop efficient numerical - Deep Learning-Based Approximation of Solutions to Stochastic Differential Equations (2026) · International Journal of Education Management and Technology · doi
Traditional numerical methods face substantial limitations in high-dimensional settings. - Solving SDEs analytically remains challenging except for special cases with specific structural properties.
generalstated in cells research gapevidence 5/5Keywords: traditional numerical methods face substantial limitations high-dimensional settings - Unconditionally positivity-preserving explicit order-one strong approximations of financial SDEs with non-Lipschitz coefficients (2026) · Journal of Computational and Applied Mathematics · doi
To further explore higher-order explicit schemes for SDEs with non-Lipschitz coefficients.
generalstated in cells future researchevidence 4/5Keywords: further explore higher-order explicit schemes sdes non-lipschitz coefficients
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