1. Overview: 4/1/13 1 2. First-Order Linear Differential Equations: 4/3/13 2 3. Examples of Integrating Factors: 4/5/13 4 4. Separation of Variables: 4/8/13 5 5. Autonomous Equations: 4/10/13 7 6. Exact Equations: 4/12/13 9 7. More Exact Equations: 4/15/13 10 8. Numerical Methods and Existence and Uniqueness: 4/17/13 11 9. Review of Weeks 1 to 3: 4/19/13 12 10. Systems of Differential Equation:...

In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.). So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreo...

Let a⊕b = max(a, b) and a⊗b = a+b for a, b ∈ R and extend the pair of operations to matrices and vectors in the same way as in linear algebra. The homogeneous twosided system in max-algebra is of the form A⊗ x = B ⊗ x. No polynomial method for solving homogeneous system is known. In this paper, we consider homogeneous twosided linear systems in max-algebra in a special case. We show that it can...

This article proposes a direct method for solving three types of integral equations with time delay. By using operational matrix of integration, integral equations can be reduced to a linear lower triangular system which can be directly solved by forward substitution. Numerical examples shows that the proposed scheme have a suitable degree of accuracy.  

this article proposes a direct method for solving three types of integral equations with time delay. by using operational matrix of integration, integral equations can be reduced to a linear lower triangular system which can be directly solved by forward substitution. numerical examples shows that the proposed scheme have a suitable degree of accuracy.

In this work, a new iterative method is proposed for obtaining the approximate solution of a class of Hammerstein type Integral Equations System. The main structure of this method is based on the Richardson iterative method for solving an algebraic linear system of equations. Some conditions for existence and unique solution of this type equations are imposed. Convergence analysis and error bou...

In this paper, a method for finding an approximate solution of a class of two-dimensional nonlinear Volterra integral equations of the first-kind is proposed. This problem is transformedto a nonlinear two-dimensional Volterra integral equation of the second-kind. The properties ofthe bivariate shifted Legendre functions are presented. The operational matrices of integrationtogether with the produ...