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Cao et al. [16] studied the implicit midpoint method and constructed a new numerical scheme for modified fractional sub-diffusion equation with nonlinear source term.
Life cycle impact assessment (LCIA) for the production of fertilizers and SWEs required for 1ha of rice cultivation was carried out using ReCiPe Midpoint method and were expressed as impacts t−1 of rice production.
In order to solve the above equations, the time step Δt is defined, and the values of acceleration, velocity and displacement are calculated in each step using the rectangle (midpoint) method and solved by MATLAB code.
Combining the implicit midpoint method and the splitting method, we present a new iterative algorithm with errors to solve the problems of finding zeros of the sum of m-accretive operators and μ-inversely strongly accretive operators in a real q-uniformly smooth and uniformly convex Banach space.
The available numerical integration methods in FORG3D are Euler method, Midpoint method and the fourth-order Runge-Kutta method [ 15].
The tree was rooted using the midpoint method and plotted using the T-REX online tool (Boc et al. 2012).
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Glass transition temperatures, T g (°C), were calculated by the inflection-midpoint method and usually reported on the first heating scans to thermally characterize the same material used in the rest of the analyses.
For a derivation of discretization errors for such parabolic type problems for a convex combination of the implicit Euler method and the midpoint method, referred to as the θ-method, the following holds (see [14]).
For the extinction and ignition processes, both the balanced splitting and midpoint method can yield accurate predictions, whereas the Strang splitting can lead to significant shifts on the ignition/extinction processes or even unphysical results.
In maple, two sub methods are available, namely trapezoidal and midpoint method.
On the contrary, the midpoint method that solves reaction and diffusion together matches the fully implicit accurate solution.
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