Exact solutions of multi-term fractional diffusion-wave equations with Robin type boundary conditions

General exact solutions in terms of wavelet expansion are obtained for multi- term time-fractional diffusion-wave equations with Robin type boundary conditions. By proposing a new method of integral transform for solving boundary value problems, such fractional partial differential equations are converted into time-fractional ordinary differ- ential equations, which are further reduced to algebraic equations by using the Laplace transform. Then, with a wavelet-based exact formula of Laplace inversion, the resulting exact solutions in the Laplace transform domain are reversed to the time-space domain. Three examples of wave-diffusion problems are given to validate the proposed analytical method.     

小波方法及其力学应用研究进展

小波理论在进行信号处理与函数逼近时体现出非常独特的时频局部性与多分辨分析能力,小波基函数则可兼具正交性、紧支性、低通滤波与插值性等优良的数学性质,这均使得小波分析理论在计算数学与计算力学领域具有很大的应用潜力,也进一步为这些领域的突破性发展带来了新的契机.自20世纪90年代以来,大量的研究已经证明,基于小波理论的数值方...     

一种适用于强非线性结构力学问题数值求解的修正小波伽辽金方法

论文通过对有限区间上的任一连续函数在边界处采用基于泰勒展开的延拓处理,构造了一种与任意边界条件相协调的改进小波尺度基函数及在此基础上建立了小波逼近格式,由此可有效避免小波逼近在求解微分方程时在边界处的跳跃或抖动问题.在此基础上,结合论文后两位作者提出的广义小波高斯积分法,关于未知函数的任意非线性项的小波展开可以显式地用...     

Exact solutions of multi-term fractional difusion-wave equations with Robin type boundary conditions

General exact solutions in terms of wavelet expansion are obtained for multiterm time-fractional difusion-wave equations with Robin type boundary conditions. By proposing a new method of integral transform for solving boundary value problems, such fractional partial diferential equations are converted into time-fractional ordinary diferential equations, which are further reduced to algebraic equations by using the Laplace transform. Then, with a wavelet-based exact formula of Laplace inversion, the resulting exact solutions in the Laplace transform domain are reversed to the time-space domain. Three examples of wave-difusion problems are given to validate the proposed analytical method.