A rank-adaptive integrator for the approximate solution of high-order tensor differential equations by tree networks is proposed and analyzed. In a recursion from leaves to root, updates bases then evolves connection tensors Galerkin method in augmented subspace spanned new old bases. This followed rank truncation within specified error tolerance. The memory requirements are linear order maxima...

Meshfree Collocation Method is used to solve linear two-dimensional problems. This method differs from weak form methods such as Galerkin method and no cellular networking and no numerical  integration. Therefore, this method has no constraints such as the integration accuracy and the integration CPU time, and equations can be isolated directly from the strong form of governing PDE. The fundame...

long time integration of large stiff systems of initial value problems, arising from chemical reactions, demands efficient methods with good accuracy and extensive absolute stability region. in this paper, we apply second derivative general linear methods to solve some stiff chemical problems such as chemical akzo nobel problem, hires problem and orego problem.