INITIAL AND BOUNDARY VALUE PROBLEMS FOR DIFFERENCE EQUATIONS

We consider initial and boundary value problems for linear nonhomogeneous difference equations with constant coefficients. For such problems we compute the numerical values of the solutions using the discrete deconvolution. The method can be easily used in applications and implemented on computer.difference equations, initial and boundary value problems, discrete convolution and deconvolution

LINEAR DISCRETE CONVOLUTION AND ITS INVERSE. PART 2. DECONVOLUTION

We present here several ways for calculating the linear discrete convolution and its inverse - the deconvolution, by direct methods, generator functions, Z-transform, using matrices and MATLAB. These notions was used by author in a series of papers, especially for solve several types of equations.complete and truncated linear discrete convolution and deconvolution

NEW APPLICATIONS OF THE ABEL-LIOUVILLE FORMULA

In a recent paper, [1], 2005, the indefinite integrals of a certain type are calculated using some linear homogeneous differential equations of second order with variable coefficients, associated with the integrals. In some simple cases, like the examples considered in this paper, the linear independent solutions of these differential equations are directly calculated relative to elementary functions. In more difficult cases, the power series method must be used. In such situations, it is advisable to use the algebraic symbolic calculus on computer. Examples of this type will be given in a subsequent paper. Because the main formula from which the integrals can be calculated is not rigorous proved in [1], we give here a correct proof based on the Abel-Liouville formula for the differential equations of second order. For completeness, we give here the proof for this formula and some of its applications, necessary to our work. Also, we included two examples.indefinite integrals, second order linear homogeneous differential equations, Abel-Liouville formula

A certain integral-recurrence equation with discrete-continuous auto-convolution

summary:Laplace transform and some of the author’s previous results about first order differential-recurrence equations with discrete auto-convolution are used to solve a new type of non-linear quadratic integral equation. This paper continues the author’s work from other articles in which are considered and solved new types of algebraic-differential or integral equations

INITIAL AND BOUNDARY VALUE PROBLEMS FOR DIFFERENCE EQUATIONS

We consider initial and boundary value problems for linear nonhomogeneous difference equations with constant coefficients. For such problems we compute the numerical values of the solutions using the discrete deconvolution. The method can be easily used in applications and implemented on computer.difference equations, initial and boundary value problems, discrete convolution and deconvolution

NEW APPLICATIONS OF THE ABEL-LIOUVILLE FORMULA

In a recent paper, [1], 2005, the indefinite integrals of a certain type are calculated using some linear homogeneous differential equations of second order with variable coefficients, associated with the integrals. In some simple cases, like the examples considered in this paper, the linear independent solutions of these differential equations are directly calculated relative to elementary functions. In more difficult cases, the power series method must be used. In such situations, it is advisable to use the algebraic symbolic calculus on computer. Examples of this type will be given in a subsequent paper. Because the main formula from which the integrals can be calculated is not rigorous proved in [1], we give here a correct proof based on the Abel-Liouville formula for the differential equations of second order. For completeness, we give here the proof for this formula and some of its applications, necessary to our work. Also, we included two examples.indefinite integrals, second order linear homogeneous differential equations, Abel-Liouville formula