On lP solutions of discrete Volterra equations.
On lP solutions of discrete Volterra equations. (Summary).
On the existence and uniqueness of solutions of a certain integral-functional equation
On the existence and uniqueness of the solution of a non-linear functional equation of r-th order
On solving systems of differential algebraic equations
In the paper the comparison method is used to prove the convergence of the Picard iterations, the Seidel iterations, as well as some modifications of these methods applied to approximate solution of systems of differential algebraic equations. The both linear and nonlinear comparison equations are emloyed.
On modification of Samoilenko's numerical-analytic method of solving boundary value problems for difference equations
In the paper a modification of Samoilenko's numerical analytic method is adapted for solving of boundary value problems for difference equation. Similarly to the case of differential equations it is shown that the considered modification of the method requires essentially less restrictive condition-then the original method-for existence and uniqueness of solution of auxiliary equations which play a crucial role in solving the boundary value problems for difference equations.
On some difference-delay equations arising in a problem of capital deposits
Introduction. We consider a real life problem: a. person has made a deposit of D0 dollars in bank B, which calculates interest on this deposit at in=100•in% after each n+l-st quarter and the interest is compounded at the end of each consecutive year since the deposit date, which means that the interest is capitalised yearly. In the case discussed the basic time unit is a quarter but the conversion period - the time interval at the end of which the interest is compounded - is four quarters (for the...
A note on the stability of -methods for Volterra integral equations of the second kind
Convergence of numerical methods for systems of neutral functional-differential-algebraic equations
A general class of numerical methods for solving initial value problems for neutral functional-differential-algebraic systems is considered. Necessary and sufficient conditions under which these methods are consistent with the problem are established. The order of consistency is discussed. A convergence theorem for a general class of methods is proved.
On numerical integration of implicit ordinary differential equations
In this paper it is shown how the numerical methods for ordinary differential equations can be adapted to implicit ordinary differential equations. The resulting methods are of the same order as the corresponding methods for ordinary differential equations. The convergence theorem is proved and some numerical examples are given.
On the existence of continuous solutions of operator equations in Banach spaces
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