| ชื่อเรื่อง | : | Accelerated numerical schemes for deterministic and stochastic partial differential equations of parabolic type |
| นักวิจัย | : | Hall, Eric Joseph |
| คำค้น | : | Richardson's method , acceleration of convergence , extrapolation to the limit , finite difference schemes , stochastic partial differential equations , partial differential equations , parabolic type , degenerate parabolic type , Cauchy problem |
| หน่วยงาน | : | Edinburgh Research Archive, United Kingdom |
| ผู้ร่วมงาน | : | Gyongy, Istvan , Sabanis, Sotirios , Engineering and Physical Sciences Research Council (EPSRC) |
| ปีพิมพ์ | : | 2556 |
| อ้างอิง | : | http://hdl.handle.net/1842/8038 |
| ที่มา | : | - |
| ความเชี่ยวชาญ | : | - |
| ความสัมพันธ์ | : | Eric Joseph Hall, "Accelerated spatial approximations for time discretized stochatic partial differential equations", SIAM J. Math. Anal., 44 (2012), pp. 3162-3185. |
| ขอบเขตของเนื้อหา | : | - |
| บทคัดย่อ/คำอธิบาย | : | First we consider implicit finite difference schemes on uniform grids in time and space for second order linear stochastic partial differential equations of parabolic type. Under sufficient regularity conditions, we prove the existence of an appropriate asymptotic expansion in powers of the the spatial mesh and hence we apply Richardson's method to accelerate the convergence with respect to the spatial approximation to an arbitrarily high order. Then we extend these results to equations where the parabolicity condition is allowed to degenerate. Finally, we consider implicit finite difference approximations for deterministic linear second order partial differential equations of parabolic type and give sufficient conditions under which the approximations in space and time can be simultaneously accelerated to an arbitrarily high order. |
| บรรณานุกรม | : |
Hall, Eric Joseph . (2556). Accelerated numerical schemes for deterministic and stochastic partial differential equations of parabolic type.
กรุงเทพมหานคร : Edinburgh Research Archive, United Kingdom . Hall, Eric Joseph . 2556. "Accelerated numerical schemes for deterministic and stochastic partial differential equations of parabolic type".
กรุงเทพมหานคร : Edinburgh Research Archive, United Kingdom . Hall, Eric Joseph . "Accelerated numerical schemes for deterministic and stochastic partial differential equations of parabolic type."
กรุงเทพมหานคร : Edinburgh Research Archive, United Kingdom , 2556. Print. Hall, Eric Joseph . Accelerated numerical schemes for deterministic and stochastic partial differential equations of parabolic type. กรุงเทพมหานคร : Edinburgh Research Archive, United Kingdom ; 2556.
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