Bäck, J., Nobile, F., Tamellini, L., Tempone, R.: Stochastic spectral Galerkin and collocation methods for PDEs with random coefficients: a numerical comparison. In: Hesthaven, J.S., Rønquist, E.M. (eds.) Spectral and high order methods for partial differential equations. Lecture N...
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inequality namely $$ \lVert abla \omega Vert_{L^{2}}^{2}\leq C\left( \lVert d\omegaVert_{L^{2}}^{2}+\lVert \delta\omegaVert_{L^{2}% }^{2}+\lVert \omegaVert_{L^{2}}^{2}ight) $$ when either $u\wedge\omega=0$ or $u\,\lrcorner\,\omega=0$ on $\partial\...
Ultimately, for more information about definitions, we suggest that readers check the book [2]. In addition, the VO fractional operator has also been used in other non-local definitions with non-singular kernels, which is beyond the scope of this review [99, 127]. 3. Physical discussion on...
Alternatively, one may directly use a numerical procedure to solve numerically the ODEs without using human intelligence for obtaining an analytical solution (which may not be possible for most real-world problems involving nonlinear ODEs/partial differential equations (PDEs)). In the latter case, ...
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