A direct method to solve integral and integro-differential equations of convolution type by using improved operational matrix

2013 ◽  
Vol 44 (6) ◽  
pp. 1173-1180 ◽  
Author(s):  
K. Maleknejad ◽  
M. Nouri
Keyword(s):  
Differential Equations ◽  
Direct Method ◽  
Operational Matrix ◽  
Convolution Type ◽  
A Direct Method

Study of B-spline collocation method for solving fractional optimal control problems

2021 ◽  
pp. 014233122098753
Author(s):  
Yousef Edrisi-Tabriz ◽  
Mehrdad Lakestani ◽  
Mohsen Razzaghi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Direct Method ◽  
Operational Matrix ◽  
Control Problems ◽  
Spline Collocation ◽  
B Spline ◽  
Fractional Optimal Control ◽  
Fractional Optimal Control Problems ◽  
A Direct Method

In this article, a class of fractional optimal control problems (FOCPs) are solved using a direct method. We present a new operational matrix of the fractional derivative in the sense of Caputo based on the B-spline functions. Then we reduce the solution of fractional optimal control problem to a nonlinear programming (NLP) one, where some existing well-developed algorithms may be applied. Numerical results demonstrate the efficiency of the presented technique.

Direct numerical method for isoperimetric fractional variational problems based on operational matrix

2017 ◽  
Vol 24 (14) ◽  
pp. 3063-3076 ◽  
Author(s):  
Samer S Ezz–Eldien ◽  
Ali H Bhrawy ◽  
Ahmed A El–Kalaawy
Keyword(s):  
Direct Method ◽  
Fractional Integration ◽  
Operational Matrix ◽  
Variational Problems ◽  
Test Problems ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Direct Numerical Method ◽  
Fractional Variational Problems ◽  
A Direct Method

In this paper, we applied a direct method for a solution of isoperimetric fractional variational problems. We use shifted Legendre orthonormal polynomials as basis function of operational matrices of fractional differentiation and fractional integration in combination with the Lagrange multipliers technique for converting such isoperimetric fractional variational problems into solving a system of algebraic equations. Also, we show the convergence analysis of the presented technique and introduce some test problems with comparisons between our numerical results with those introduced using different methods.

To Investigate the Euler Solution of Differential Equation

2014 ◽  
Vol 614 ◽  
pp. 409-412
Author(s):  
Lin Long Zhao
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Euler Equations ◽  
Direct Method ◽  
Special Solution ◽  
Linear Differential Equations ◽  
Linear Differential ◽  
Euler Solution ◽  
A Direct Method

For Euler Equations L(y）=∑aixiy(i) =f(x)are Given Special Solution of a Direct Method, and a Special Coefficient Linear Differential Equations L(y)=∑aiy(i)=∑bjejx into Ordinary Differential Equations Euler.

Origin of Generating Functions in Applied Mechanics

1969 ◽  
Vol 36 (4) ◽  
pp. 875-877 ◽  
Author(s):  
P. E. Wilson ◽  
J. F. Hook
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Generating Functions ◽  
Shell Theory ◽  
Direct Method ◽  
Applied Mechanics ◽  
Linear Partial Differential Equations ◽  
Dependent Variables ◽  
Constant Coefficients ◽  
A Direct Method

This Note presents a direct method by which the equations satisfied by generating functions and their relations to the original dependent variables can be deduced. The technique given is applicable to systems of linear partial differential equations with constant coefficients. Examples are presented from the fields of elasticity and shell theory.

scholarly journals A Direct Method of using the Hodograph Plane in Fluid Dynamics

1958 ◽  
Vol 11 (2) ◽  
pp. 107-114
Author(s):  
A. G. Mackie
Keyword(s):  
Fluid Dynamics ◽  
Fixed Point ◽  
Differential Equations ◽  
Direct Method ◽  
Rectilinear Motion ◽  
Hodograph Method ◽  
Independent Variables ◽  
Underlying Principle ◽  
Hodograph Plane ◽  
A Direct Method

The application of the hodograph method in problems in fluid dynamics dates back to the time of Helmholtz and Kirchhoff. The underlying principle is simple. It is in effect to rewrite the governing differential equations with the roles of the original dependent and independent variables reversed. Such a procedure is not uncommon in problems depending upon ordinary differential equations. For example, if the velocity of a particle in rectilinear motion is prescribed as a function of distance from a fixed point, the problem of finding the relation between its position and the time t can be solved by one quadrature if t is regarded as the dependent variable.

scholarly journals Direct method for variational problems via hybrid of block-pulse and chebyshev functions

2000 ◽  
Vol 6 (1) ◽  
pp. 85-97 ◽  
Author(s):  
Mohsen Razzaghi ◽  
Hamid-Reza Marzban
Keyword(s):  
Direct Method ◽  
Operational Matrix ◽  
Variational Problems ◽  
Cross Product ◽  
Hybrid Functions ◽  
Block Pulse Functions ◽  
Hybrid Function ◽  
Operational Matrix Of Integration ◽  
A Direct Method ◽  
Two Hybrid

A direct method for finding the solution of variational problems using a hybrid function is discussed. The hybrid functions which consist of block-pulse functions plus Chebyshev polynomials are introduced. An operational matrix of integration and the integration of the cross product of two hybrid function vectors are presented and are utilized to reduce a variational problem to the solution of an algebraic equation. Illustrative examples are included to demonstrate the validity and applicability of the technique.

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