Fractional stochastic evolution equations often arise in theory and applications. Finding exact solutions of such equations is impossible in most cases. In this paper, our main goal is to establish the existence and uniqueness of mild solutions of the equations, and give a numerical method for approximating such mild solutions. The numerical method is based on a combination of subspaces decomposition technique and waveform relaxation method, which is called a frequency decomposition waveform relaxation method. Moreover, the convergence of the frequency decomposition waveform relaxation method is discussed in detail. Finally, several illustrative examples are presented to confirm the validity and applicability of the proposed numerical method.
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September 2019
Research-Article
Analysis and Numerical Solutions for Fractional Stochastic Evolution Equations With Almost Sectorial Operators
Xiao-Li Ding,
Xiao-Li Ding
Department of Mathematics,
Xi'an Polytechnic University,
Xi'an, Shaanxi 710048, China
e-mail: dingding0605@126.com
Xi'an Polytechnic University,
Xi'an, Shaanxi 710048, China
e-mail: dingding0605@126.com
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Juan J. Nieto
Juan J. Nieto
Departamento de Análisis Matemático,
Facultad de Matemáticas,
Universidad de Santiago de Compostela,
Santiago de Compostela 15782, Spain
e-mail: juanjose.nieto.roig@usc.es
Facultad de Matemáticas,
Universidad de Santiago de Compostela,
Santiago de Compostela 15782, Spain
e-mail: juanjose.nieto.roig@usc.es
Search for other works by this author on:
Xiao-Li Ding
Department of Mathematics,
Xi'an Polytechnic University,
Xi'an, Shaanxi 710048, China
e-mail: dingding0605@126.com
Xi'an Polytechnic University,
Xi'an, Shaanxi 710048, China
e-mail: dingding0605@126.com
Juan J. Nieto
Departamento de Análisis Matemático,
Facultad de Matemáticas,
Universidad de Santiago de Compostela,
Santiago de Compostela 15782, Spain
e-mail: juanjose.nieto.roig@usc.es
Facultad de Matemáticas,
Universidad de Santiago de Compostela,
Santiago de Compostela 15782, Spain
e-mail: juanjose.nieto.roig@usc.es
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received January 27, 2019; final manuscript received April 30, 2019; published online June 10, 2019. Assoc. Editor: Dumitru Baleanu.
J. Comput. Nonlinear Dynam. Sep 2019, 14(9): 091001 (12 pages)
Published Online: June 10, 2019
Article history
Received:
January 27, 2019
Revised:
April 30, 2019
Citation
Ding, X., and Nieto, J. J. (June 10, 2019). "Analysis and Numerical Solutions for Fractional Stochastic Evolution Equations With Almost Sectorial Operators." ASME. J. Comput. Nonlinear Dynam. September 2019; 14(9): 091001. https://doi.org/10.1115/1.4043725
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