scholarly journals Limit theorems for solutions of stochastic differential equation problems

1980 ◽  
Vol 3 (1) ◽  
pp. 113-149 ◽  
Author(s):  
J. Vom Scheidt ◽  
W. Purkert
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Initial Value Problems ◽  
Limit Theorems ◽  
Eigenvalue Problems ◽  
Random Processes ◽  
Inhomogeneous Term ◽  
Initial Value ◽  
Linear Differential

In this paper linear differential equations with random processes as coefficients and as inhomogeneous term are regarded. Limit theorems are proved for the solutions of these equations if the random processes are weakly correlated processes.Limit theorems are proved for the eigenvalues and the eigenfunctions of eigenvalue problems and for the solutions of boundary value problems and initial value problems.

scholarly journals Projector Approach to Constructing Asymptotic Solution of Initial Value Problems for Singularly Perturbed Systems in Critical Case

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 56 ◽  
Author(s):  
Galina Kurina
Keyword(s):  
Differential Equations ◽  
Asymptotic Solution ◽  
Initial Value Problems ◽  
Singular Matrix ◽  
Singularly Perturbed Systems ◽  
English Transl ◽  
Initial Value ◽  
Boundary Functions ◽  
Linear Differential ◽  
Orthogonal Projectors

Under some conditions, an asymptotic solution containing boundary functions was constructed in a paper by Vasil’eva and Butuzov (Differ. Uravn. 1970, 6(4), 650–664 (in Russian); English transl.: Differential Equations 1971, 6, 499–510) for an initial value problem for weakly non-linear differential equations with a small parameter standing before the derivative, in the case of a singular matrix A ( t ) standing in front of the unknown function. In the present paper, the orthogonal projectors onto k e r A ( t ) and k e r A ( t ) ′ (the prime denotes the transposition) are used for asymptotics construction. This approach essentially simplifies understanding of the algorithm of asymptotics construction.

scholarly journals On the correct formulation of a nonlinear differential equations in Banach space

2001 ◽  
Vol 26 (7) ◽  
pp. 437-444
Author(s):  
Mahmoud M. El-Borai ◽  
Osama L. Moustafa ◽  
Fayez H. Michael
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Existence And Uniqueness ◽  
Initial Value Problems ◽  
Nonlinear Differential Equations ◽  
Initial Value ◽  
Correct Formulation

We study, the existence and uniqueness of the initial value problems in a Banach spaceEfor the abstract nonlinear differential equation(dn−1/dtn−1)(du/dt+Au)=B(t)u+f(t,W(t)), and consider the correct solution of this problem. We also give an application of the theory of partial differential equations.

Fuzzy form of Euler Method to Solve Fuzzy Differential Equations

2021 ◽  
Vol 01 ◽  
Author(s):  
Umme Salma Pirzada ◽  
S. Rama Mohan
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Riccati Equation ◽  
Initial Value Problems ◽  
Euler Method ◽  
Fuzzy Differential Equation ◽  
Fuzzy Arithmetic ◽  
Local Error ◽  
Initial Value

: This paper proposes fuzzy form of Euler method to solve fuzzy initial value problems. By this method, fuzzy differential equations can be solved directly using fuzzy arithmetic. The solution by this method is readily available in a form of fuzzy-valued function. The method does not require to re-write fuzzy differential equation into system of two crisp ordinary differential equations. Algorithm of the method and local error expression are discussed. An illustration and solution of fuzzy Riccati equation are provided for the applicability of the method.

scholarly journals Solving Ordinary Differential Equation of Higher Order by Adomian Decomposition Method

2020 ◽  
pp. 44-53
Author(s):  
Sumayah Ghaleb Othman ◽  
Yahya Qaid Hasan
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Initial Value Problems ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Higher Order ◽  
Initial Value ◽  
Adomian Decomposition ◽  
Different Types

Aims/ Objectives: In this article, we use Adomian Decomposition method (ADM) for solving initial value problems in the higher order ordinary differential equations. Many researchers have used the ADM in order to find convergent as well as exact solutions of different types of equations. Therefore, the ADM is considered as an effective and successful method for solving differential equations. In this paper, we presented some suggested amendments to the ADM by using a new differential operator in order to find solutions for higher order types of equations. We demonstrated the effectiveness of this method through many examples and we find out that we get an approximate solutions using the proposed amendments. We can conclude that the suggested modification of ADM is afftective and produces reliable results.

scholarly journals Numerical solution of linear differential equations by Walsh polynomials approach

2020 ◽  
Vol 57 (2) ◽  
pp. 217-254
Author(s):  
◽  
Rodolfo Toledo
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Harmonic Analysis ◽  
Initial Value Problems ◽  
Linear Differential Equations ◽  
Previous Article ◽  
Initial Value ◽  
Constant Coefficients ◽  
Linear Differential

AbstractIn 1975 C. F. Chen and C. H. Hsiao established a new procedure to solve initial value problems of systems of linear differential equations with constant coefficients by Walsh polynomials approach. However, they did not deal with the analysis of the proposed numerical solution. In a previous article we study this procedure in case of one equation with the techniques that the theory of dyadic harmonic analysis provides us. In this paper we extend these results through the introduction of a new procedure to solve initial value problems of differential equations with not necessarily constant coefficients.

Klein's Oscillation Theorem for Periodic Boundary Conditions

1971 ◽  
Vol 23 (4) ◽  
pp. 699-703 ◽  
Author(s):  
A. Howe
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Eigenvalue Problems ◽  
Periodic Boundary Conditions ◽  
Linear Differential Equations ◽  
Oscillation Theorem ◽  
Linear Differential ◽  
Image Position

Multiparameter eigenvalue problems for systems of linear differential equations with homogeneous boundary conditions have been considered by Ince [4] and Richardson [5, 6], and more recently Faierman [3] has considered their completeness and expansion theorems. A survey of eigenvalue problems with several parameters, in mathematics, is given by Atkinson [1].We consider the two differential equations:1a1bwhere p1’(x), q1(x), A1(x), B1(x) and p2’(y), q2(y), A2(y), B2(y) are continuous for x ∈ [a1, b1] and y ∈ [a2, b2] respectively, and p1 (x) > 0(x ∈ [a1, b1]), p2(y) > 0 (y ∈ [a2, b2]), p1(a1) = p1(b1), p2(a2) = p2(b2). The differential equations (1) will be subjected to the periodic boundary conditions.2a2bLet us consider a single differential equation

scholarly journals Modified New Iterative Method for Solving Nonlinear Partial Differential Equations

2020 ◽  
Vol 19 ◽  
pp. 1-10
Author(s):  
Alaa K. Jabber
Keyword(s):  
Differential Equation ◽  
Differential Operator ◽  
Iterative Method ◽  
Initial Value Problems ◽  
Linear Differential Operator ◽  
Nonlinear Partial Differential Equations ◽  
Initial Value ◽  
The Laplace Transform ◽  
Linear Differential ◽  
New Iterative Method

In this paper, the iterative method, proposed by Gejji and Jafari in 2006, has been modified for solving nonlinear initial value problems. The Laplace transform was used in this modification to eliminate the linear differential operator in the differential equation. The convergence of the solution was discussed according to the modification proposed. To illustrate this modification some examples were presented.

scholarly journals On the boundedness of solution of the second order ordinary differential equation with damping term and involution

2021 ◽  
Vol 102 (2) ◽  
pp. 16-24
Author(s):  
A. Ashyralyev ◽  
◽  
M. Ashyralyyeva ◽  
O. Batyrova ◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Initial Value Problem ◽  
Second Order ◽  
Stability Estimates ◽  
Damping Term ◽  
Initial Value ◽  
Order Ordinary Differential Equation ◽  
Linear Differential

In the present paper the initial value problem for the second order ordinary differential equation with damping term and involution is investigated. We obtain equivalent initial value problem for the fourth order ordinary differential equations to the initial value problem for second order linear differential equations with damping term and involution. Theorem on stability estimates for the solution of the initial value problem for the second order ordinary linear differential equation with damping term and involution is proved. Theorem on existence and uniqueness of bounded solution of initial value problem for second order ordinary nonlinear differential equation with damping term and involution is established.

Sign in / Sign up

Export Citation Format

Share Document