中国物理B ›› 2023, Vol. 32 ›› Issue (3): 30202-030202.doi: 10.1088/1674-1056/ac9368

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Adaptive multi-step piecewise interpolation reproducing kernel method for solving the nonlinear time-fractional partial differential equation arising from financial economics

Ming-Jing Du(杜明婧)1,†, Bao-Jun Sun(孙宝军)1, and Ge Kai(凯歌)2   

  1. 1 School of Computer Information Management, Inner Mongolia University of Finance and Economics, Hohhot 010070, China;
    2 School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010070, China
  • 收稿日期:2022-06-05 修回日期:2022-09-01 接受日期:2022-09-21 出版日期:2023-02-14 发布日期:2023-03-01
  • 通讯作者: Ming-Jing Du E-mail:724297269@qq.com
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 71961022, 11902163, 12265020, and 12262024), the Natural Science Foundation of Inner Mongolia Autonomous Region of China (Grant Nos. 2019BS01011 and 2022MS01003), 2022 Inner Mongolia Autonomous Region Grassland Talents Project-Young Innovative and Entrepreneurial Talents (Mingjing Du), 2022 Talent Development Foundation of Inner Mongolia Autonomous Region of China (Ming-Jing Du), the Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region Program (Grant No. NJYT-20-B18), the Key Project of High-quality Economic Development Research Base of Yellow River Basin in 2022 (Grant No. 21HZD03), 2022 Inner Mongolia Autonomous Region International Science and Technology Cooperation High-end Foreign Experts Introduction Project (Ge Kai), and MOE (Ministry of Education in China) Humanities and Social Sciences Foundation (Grants No. 20YJC860005).

Adaptive multi-step piecewise interpolation reproducing kernel method for solving the nonlinear time-fractional partial differential equation arising from financial economics

Ming-Jing Du(杜明婧)1,†, Bao-Jun Sun(孙宝军)1, and Ge Kai(凯歌)2   

  1. 1 School of Computer Information Management, Inner Mongolia University of Finance and Economics, Hohhot 010070, China;
    2 School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010070, China
  • Received:2022-06-05 Revised:2022-09-01 Accepted:2022-09-21 Online:2023-02-14 Published:2023-03-01
  • Contact: Ming-Jing Du E-mail:724297269@qq.com
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 71961022, 11902163, 12265020, and 12262024), the Natural Science Foundation of Inner Mongolia Autonomous Region of China (Grant Nos. 2019BS01011 and 2022MS01003), 2022 Inner Mongolia Autonomous Region Grassland Talents Project-Young Innovative and Entrepreneurial Talents (Mingjing Du), 2022 Talent Development Foundation of Inner Mongolia Autonomous Region of China (Ming-Jing Du), the Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region Program (Grant No. NJYT-20-B18), the Key Project of High-quality Economic Development Research Base of Yellow River Basin in 2022 (Grant No. 21HZD03), 2022 Inner Mongolia Autonomous Region International Science and Technology Cooperation High-end Foreign Experts Introduction Project (Ge Kai), and MOE (Ministry of Education in China) Humanities and Social Sciences Foundation (Grants No. 20YJC860005).

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摘要： This paper is aimed at solving the nonlinear time-fractional partial differential equation with two small parameters arising from option pricing model in financial economics. The traditional reproducing kernel (RK) method which deals with this problem is very troublesome. This paper proposes a new method by adaptive multi-step piecewise interpolation reproducing kernel (AMPIRK) method for the first time. This method has three obvious advantages which are as follows. Firstly, the piecewise number is reduced. Secondly, the calculation accuracy is improved. Finally, the waste time caused by too many fragments is avoided. Then four numerical examples show that this new method has a higher precision and it is a more timesaving numerical method than the others. The research in this paper provides a powerful mathematical tool for solving time-fractional option pricing model which will play an important role in financial economics.

关键词: time-fractional partial differential equation, adaptive multi-step, reproducing kernel method method, numerical solution

Abstract: This paper is aimed at solving the nonlinear time-fractional partial differential equation with two small parameters arising from option pricing model in financial economics. The traditional reproducing kernel (RK) method which deals with this problem is very troublesome. This paper proposes a new method by adaptive multi-step piecewise interpolation reproducing kernel (AMPIRK) method for the first time. This method has three obvious advantages which are as follows. Firstly, the piecewise number is reduced. Secondly, the calculation accuracy is improved. Finally, the waste time caused by too many fragments is avoided. Then four numerical examples show that this new method has a higher precision and it is a more timesaving numerical method than the others. The research in this paper provides a powerful mathematical tool for solving time-fractional option pricing model which will play an important role in financial economics.

Key words: time-fractional partial differential equation, adaptive multi-step, reproducing kernel method method, numerical solution

中图分类号:  (Numerical simulation; solution of equations)

  • 02.60.Cb
02.60.-x (Numerical approximation and analysis) 02.30.Jr (Partial differential equations)