English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this work, in order to obtain higher-order schemes for solving forwardbackward stochastic differential equations, we adopt the high-order multi-stepmethod in [W. Zhao, Y. Fu and T. Zhou, SIAM J. Sci. Comput., 36(4) (2014),pp.A1731-A1751] by combining multi-steps. Two reference ordinary differentialequations containing the conditional expectations and their derivatives arederived from the backward component. These derivatives are approximated byfinite difference methods with multi-step combinations. The resulting scheme isa semi-discretization in the time direction involving conditional expectations,which are solved by using the Gaussian quadrature rules and polynomialinterpolations on the spatial grids. Our new proposed multi-step scheme allowsfor higher convergence rate up to ninth order, and are more efficient. Finally,we provide a numerical illustration of the convergence of the proposed method.

High-order combined Multi-step Scheme for solving forward Backward Stochastic Differential Equations