Stochastic symplectic methods based on the Padé approximations for linear stochastic Hamiltonian systems

详细信息    查看全文

• 作者：Liying Sun ; Lijin Wang ; ^{ljwang@ucas.ac.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Padé ; approximation ; Linear stochastic Hamiltonian systems ; Symplectic methods ; Root-mean-square convergence order
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：311
• 期：Complete
• 页码：439-456
• 全文大小：725 K

文摘

In this article, we propose a kind of numerical methods based on the Padé approximations, for two kinds of stochastic Hamiltonian systems. For the general linear stochastic Hamiltonian systems, it is shown that the applied Padé approximations mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716303715&_mathId=si1.gif&_user=111111111&_pii=S0377042716303715&_rdoc=1&_issn=03770427&md5=b7bc20ec7362aea9208e13acd15aedba" title="Click to view the MathML source">P_(k,k)mathContainer hidden">mathCode"><math altimg="si1.gif" overflow="scroll">P(k,k)math> produce numerical solutions that are symplectic, and the proposed numerical schemes based on mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716303715&_mathId=si2.gif&_user=111111111&_pii=S0377042716303715&_rdoc=1&_issn=03770427&md5=c2c2d5d19f9727bbcdc39242a27d806e" title="Click to view the MathML source">P_(r,s)mathContainer hidden">mathCode"><math altimg="si2.gif" overflow="scroll">P(r,s)math> are of root-mean-square convergence order mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716303715&_mathId=si3.gif&_user=111111111&_pii=S0377042716303715&_rdoc=1&_issn=03770427&md5=d468e31eb6b8c63f3e0592d5261109d4">mage" height="19" width="21" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0377042716303715-si3.gif">mathContainer hidden">mathCode"><math altimg="si3.gif" overflow="scroll">r+s2math>. For a special kind of linear stochastic Hamiltonian systems with additive noises, the numerical methods using two kinds of Padé approximations, mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716303715&_mathId=si4.gif&_user=111111111&_pii=S0377042716303715&_rdoc=1&_issn=03770427&md5=a2af92b2fee57c67d6d683cc09dc86b7">mage" height="17" width="31" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0377042716303715-si4.gif">mathContainer hidden">mathCode"><math altimg="si4.gif" overflow="scroll">P(rˆ,sˆ)math> and mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716303715&_mathId=si5.gif&_user=111111111&_pii=S0377042716303715&_rdoc=1&_issn=03770427&md5=38ad848c5d42e082f6978a94c15f8d73">mage" height="17" width="33" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0377042716303715-si5.gif">mathContainer hidden">mathCode"><math altimg="si5.gif" overflow="scroll">P(ř,1)math>, possess root-mean-square convergence order mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716303715&_mathId=si6.gif&_user=111111111&_pii=S0377042716303715&_rdoc=1&_issn=03770427&md5=f9ed9319cf9d189387ebd05e874a3b1b">mage" height="13" width="37" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0377042716303715-si6.gif">mathContainer hidden">mathCode"><math altimg="si6.gif" overflow="scroll">ř+2math> when mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716303715&_mathId=si7.gif&_user=111111111&_pii=S0377042716303715&_rdoc=1&_issn=03770427&md5=0445a13bdd0d78e4980f3dc7b6c9753b">mage" height="13" width="93" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0377042716303715-si7.gif">mathContainer hidden">mathCode"><math altimg="si7.gif" overflow="scroll">rˆ+sˆ=ř+3math>, and are symplectic if mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716303715&_mathId=si8.gif&_user=111111111&_pii=S0377042716303715&_rdoc=1&_issn=03770427&md5=5c3e8d5aec19a42e31ae43d87a9ef353">mage" height="12" width="37" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0377042716303715-si8.gif">mathContainer hidden">mathCode"><math altimg="si8.gif" overflow="scroll">rˆ=sˆmath>. These generalize the Padé approximation approaches for symplectic integration of linear Hamiltonian systems to the stochastic context.