Abstract: In this work we present a family of new convergent
type methods splitting high order no negative steps feature that
allows your application to irreversible problems. Performing affine
combinations consist of results obtained with Trotter Lie integrators
of different steps. Some examples where applied symplectic
compared with methods, in particular a pair of differential equations
semilinear. The number of basic integrations required is comparable
with integrators symplectic, but this technique allows the ability
to do the math in parallel thus reducing the times of which
exemplify exhibiting some implementations with simple schemes for
its modularity and scalability process.
Abstract: In this paper, a nonconforming mixed finite element method is studied for semilinear pseudo-hyperbolic partial integrodifferential equations. By use of the interpolation technique instead of the generalized elliptic projection, the optimal error estimates of the corresponding unknown function are given.
Abstract: Semilinear elliptic equations are ubiquitous in natural sciences. They give rise to a variety of important phenomena in quantum mechanics, nonlinear optics, astrophysics, etc because they have rich multiple solutions. But the nontrivial solutions of semilinear equations are hard to be solved for the lack of stabilities, such as Lane-Emden equation, Henon equation and Chandrasekhar equation. In this paper, bifurcation method is applied to solving semilinear elliptic equations which are with homogeneous Dirichlet boundary conditions in 2D. Using this method, nontrivial numerical solutions will be computed and visualized in many different domains (such as square, disk, annulus, dumbbell, etc).