二维分数次Legendre小波求解变时间分数阶微分方程  

TWO-DIMENSIONAL FRACTIONAL-ORDER LEGENDRE WAVELETS FOR SOLVING VARIABLE-ORDER TIME FRACTIONAL DIFFERENTIAL EQUATIONS

作　　者：周凤英 张嘉堃 黄英杰 Zhou Fengying;Zhang Jiakun;Huang Yingjie(School of Mathematics and Computer Science,Jiangci Science and Technology Normal University,Nanchang 330036,China)

机构地区：[1]江西科技师范大学大数据科学学院,南昌330036

出　　处：《数值计算与计算机应用》2024年第4期354-372,共19页Journal on Numerical Methods and Computer Applications

基　　金：江西省自然科学基金项目(20202BABL201006);江西科技师范大学博士科研启动基金项目(2023BSQD23)资助.

摘　　要：基于二维分数次Legendre小波(FOLWs),本文提出了一种求解变时间分数阶微分方程的数值方法在Riemann-Liouville(R-L)变分数阶积分意义下,利用单位阶跃函数和正则化β函数导出了FOLWs的变分数阶积分公式.基于广义分数次Taylor展开,研究了二维FOLWs展开的误差估计.通过FOLWs的变分数阶积分公式以及有效的配置法,变时间分数阶微分方程离散化为代数方程组.然后,分别用Gauss消去法和Picard迭代法解得问题线性和非线性两种情况下的解.本文若干数值算例也验证了该数值方法的有效性、适用性和高精度性.A numerical method for solving variable-order time fractional differential equations is developed by using two-dimensional fractional-order Legendre wavelets(FOLWs).In the sense of Riemann-Liouville(R-L)variable fractional-order integral,the variable fractionalorder integral formulas of FOLWs are derived by means of unit step function and regularizedβfunction.Based on the generalized fractional-order Taylor expansion,the error estimation of two-dimensional FOLWs expansion is studied.The variable-order time fractional differential equation is discretized into a system of algebraic equation by using the collocation method.The resulted linear and nonlinear system are solved by Gauss elimination method and Picard iterative method,respectively.The effectiveness,applicability and accuracy of the proposed method are verified by several numerical examples.

关 键 词：Riemann-Liouville分数阶积分 Caputo分数阶微分 分数次Legendre小波 变时间分数阶微分方程 配置法 

分 类 号：O241.8[理学—计算数学]