Numerical solution of high order linear complex differential equations via complex operational matrix method

SeMA Journal ◽  
2018 ◽  
Vol 76 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Farshid Mirzaee ◽  
Nasrin Samadyar ◽  
Sahar Alipour
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Matrix Method ◽  
Operational Matrix ◽  
High Order ◽  
Linear Complex ◽  
Order Linear ◽  
Operational Matrix Method ◽  
Complex Differential Equations

scholarly journals A Collocation Method Based on the Bernoulli Operational Matrix for Solving High-Order Linear Complex Differential Equations in a Rectangular Domain

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Faezeh Toutounian ◽  
Emran Tohidi ◽  
Stanford Shateyi
Keyword(s):  
Differential Equations ◽  
Matrix Equation ◽  
Operational Matrix ◽  
Bernoulli Polynomials ◽  
High Order ◽  
Linear Complex ◽  
Order Linear ◽  
Linear Algebraic Equations ◽  
The Matrix ◽  
Complex Differential Equations

This paper contributes a new matrix method for the solution of high-order linear complex differential equations with variable coefficients in rectangular domains under the considered initial conditions. On the basis of the presented approach, the matrix forms of the Bernoulli polynomials and their derivatives are constructed, and then by substituting the collocation points into the matrix forms, the fundamental matrix equation is formed. This matrix equation corresponds to a system of linear algebraic equations. By solving this system, the unknown Bernoulli coefficients are determined and thus the approximate solutions are obtained. Also, an error analysis based on the use of the Bernoulli polynomials is provided under several mild conditions. To illustrate the efficiency of our method, some numerical examples are given.

scholarly journals A new numerical approach for solving high-order linear and non-linear differantial equations

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 67-77
Author(s):  
Aydin Secer ◽  
Selvi Altun
Keyword(s):  
Matrix Method ◽  
Operational Matrix ◽  
Numerical Approach ◽  
High Order ◽  
Algebraic Equations ◽  
Practical Application ◽  
Order Linear ◽  
Operational Matrix Method ◽  
Non Linear ◽  
Linear Problems

In this paper, the Legendre wavelet operational matrix method has been introduced for solving high-order linear and non-linear multi-point: initial and boundary value problems. It has been suggested that the technique is rest upon practical application of the operational matrix and its derivatives. The differential equation is presented that it is converted to a system of algebraic equations via the properties of Legendre wavelet together with the operational matrix method. As a result of this study, the scheme has been tested on five linear and non-linear problems. The results have demonstrated that this method is a very effective and advantageous tool in solving such problems.

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