Volume 42 Issue 6
Jun.  2021
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ZHANG Man, CAO Yanhua, YANG Xiaozhong. Numerical Analysis of a Class of Fractional Langevin Equations With the Block-by-Block Method[J]. Applied Mathematics and Mechanics, 2021, 42(6): 562-574. doi: 10.21656/1000-0887.410337
Citation: ZHANG Man, CAO Yanhua, YANG Xiaozhong. Numerical Analysis of a Class of Fractional Langevin Equations With the Block-by-Block Method[J]. Applied Mathematics and Mechanics, 2021, 42(6): 562-574. doi: 10.21656/1000-0887.410337

Numerical Analysis of a Class of Fractional Langevin Equations With the Block-by-Block Method

doi: 10.21656/1000-0887.410337
  • Received Date: 2020-10-29
  • Rev Recd Date: 2020-11-21
  • The fractional Langevin equation is of great scientific significance and engineering application value. Based on the classical block-by-block method, the numerical solution of a class of fractional Langevin equations with Caputo derivatives was obtained. Through introduction of the quadratic Lagrange basis function interpolation, the block-by-block convergent nonlinear equations were constructed, and the numerical solution of the Langevin equation was obtained by coupling in each block. Under the condition of 0<α<1, the stochastic Taylor expansion was used to prove that the block-by-block method is (3+α)-order convergent. Numerical experiments show that, the block-by-block method is stable and convergent under different values of α and time step h,and overcomes the existing methods’ disadvantages of slow speed and poor accuracy for solving fractional Langevin equations.
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