Chaotic characteristics analysis of the sintering process system with unknown dynamic functions based on phase space reconstruction and chaotic invariables

We develop a local discontinuous Galerkin finite element method for the distributed-order time and Riesz space-fractional convection–diffusion and Schrödinger-type equations. The stability of the presented schemes is proved and optimal order of convergence (mathcal {O}(h^{N+1}+(Delta t)^{1+frac{theta }{2}}+theta ^{2})) for the Riesz space-fractional diffusion and Schrödinger-type equations with distributed order in time, an order of convergence of (mathcal {O}(h^{N+frac{1}{2}}+(Delta t)^{1+frac{theta }{2}}) (+theta ^{2})) is provided for the Riesz space-fractional convection–diffusion equations with distributed order in time where h, (theta ) and (Delta t) are space step size, the distributed-order variables and the step sizes in time, respectively. Finally, the performed numerical examples confirm the optimal convergence order and illustrate the effectiveness of the method.