By adding a suitable real function on both sides of the quadratic Riccati differential equation, we propose a weighted type of Adams-Bashforth rules for solving it, in which moments are used instead of the constant coefficients of Adams-Bashforth rules. Numerical results reveal that the proposed method is efficient and can be applied for other nonlinear problems.

Stochastic linear combinations of some random vectors are studied where the dis-tribution of the random vectors and the joint distribution of their coe, cients have Dirichlet distributions. A method is provided for calculating the distribution of these combinations which has been studied before. Our main result is the same as but from a di, erent point of view.

Many quick-link optimization models of transferring corrosive materials, need some constraints to change the output space such that all of the criteria are met, which forms a nonlinear problem with speci, c constraints. So we use an approach for , nding global solutions of mixed-integer nonlinear optimization problems with ordinary di, erential equation constraints on the shortest path problem connective body composition because we need to save time. For the solution of constrained di, erential equations, we present a numerical method by coupling an implicit numerical method, and the results will be expressed by showing that the optimal path is selected.

We consider a , rst-order partial di, erential equation with constant irreversible co-e, cients in a Banach space in the regular case. The equation is split into equations in subspaces, in which non-degenerate subsystems are obtained. We obtain an ana-lytical solution of each system with Showalter-type conditions. Finally, an example is given to illustrate the theoretical results.

In this paper, we propose a new numerical algorithm for the approximate solution of non-homogeneous fractional di, erential equation. Using this algorithm the fractional di, erential equations are transformed into a system of algebraic linear equations by operational matrices of block-pulse and hybrid functions. Based on our new algorithm, this system of algebraic linear equations can be solved by a proposed (TSI) method. Further, some numerical examples are given to illustrate and establish the accuracy and reliability of the proposed algorithm.