Iterative reproducing kernel Hilbert spaces method for Riccati differential equations

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• 作者：Mehmet Giyas Sakar ^{giyassakar@hotmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Iterative reproducing kernel Hilbert space method ; Inner product ; Riccati differential equation ; Analytic approximation ; Variable coefficient
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：309
• 期：Complete
• 页码：163-174
• 全文大小：516 K

文摘

This paper presents iterative reproducing kernel Hilbert spaces method (IRKHSM) to obtain the numerical solutions for Riccati differential equations with constant and variable coefficients. Representation of the exact solution is given in the class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716303016&_mathId=si16.gif&_user=111111111&_pii=S0377042716303016&_rdoc=1&_issn=03770427&md5=55a76f6ffef0cb7dfcf85ad57d355c2f">class="imgLazyJSB inlineImage" height="19" width="62" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0377042716303016-si16.gif">class="mathContainer hidden">class="mathCode">$W_2^2[0,X]$ reproducing kernel space. Numerical solution of Riccati differential equations is acquired by interrupting the class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716303016&_mathId=si17.gif&_user=111111111&_pii=S0377042716303016&_rdoc=1&_issn=03770427&md5=4ae4fc990beefbce96e48a680bda7203" title="Click to view the MathML source">nclass="mathContainer hidden">class="mathCode">$n$-term of the exact solution. Also, the error of the numerical solution is monotone decreasing in terms of the norm of class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716303016&_mathId=si16.gif&_user=111111111&_pii=S0377042716303016&_rdoc=1&_issn=03770427&md5=55a76f6ffef0cb7dfcf85ad57d355c2f">class="imgLazyJSB inlineImage" height="19" width="62" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0377042716303016-si16.gif">class="mathContainer hidden">class="mathCode">$W_2^2[0,X]$. The outcomes from numerical examples show that the present iterative algorithm is very effective and convenient.