The paper presents fourth order Runge–Kutta methods derived from symmetric Hermite–Obreshkov schemes by suitably approximating the involved higher derivatives. In particular, starting multi-derivative extension of midpoint method we have obtained a new implicit four, for numerical solution first-order differential equations. is symplectic and suitable both initial boundary value Hamiltonian pro...

We started our research with the intent on answering the following question: can we find a way to calculate all the subgroups of the symmetric group. This is easier said that done, as the number of subgroups for a symmetric group grows quickly with each successive symmetric group. This problem can actually be simplified to finding the subgroup conjugacy classes. So now we have the slightly diff...

We propose an adaptation of the Feasible Direction Interior Points Algorithm (FDIPA) J. Herskovits, for solving large-scale linear programs. At each step, solution two systems with same coefficient matrix is determined. This step involves a significant computational effort. Reducing time is, therefore, way to improve performance method. The be solved are associated definite positive symmetric m...

We study the geometry of Gorenstein curve singularities genus two, and their stable limits. These come in two families, corresponding to either Weierstrass or conjugate points on a semistable tail. For every $1\leq m <n$, stability condition - using one markings as reference point, therefore not $\mathfrak S_n$-symmetric defines proper Deligne-Mumford stacks $\overline{\mathcal M}_{2,n}^{(m)}$ ...

A new parallel symmetric successive over-relaxation (PSSOR) preconditioner is proposed in this paper by the multi-type partition techniques introduced in SIAM J. Scientific Computing 20, 2006, pp. 1513-1533. In a general matrix expression, it is proved to be symmetric and positive-definite if the coefficient matrix of a linear system is symmetric and positive-definite. It is also proved to be e...

We consider the problem of solving a linear system Ax = b when A is nearly symmetric and when the system is preconditioned by a symmetric positive definite matrix M . In the symmetric case, we can recover symmetry by using M -inner products in the conjugate gradient (CG) algorithm. This idea can also be used in the nonsymmetric case, and near symmetry can be preserved similarly. Like CG, the ne...