scholarly journals Chebyshev operational matrix method for solving multi-order fractional ordinary differential equations

2013 ◽  
Vol 37 (20-21) ◽  
pp. 8903-8911 ◽  
Author(s):  
M.H. Atabakzadeh ◽  
M.H. Akrami ◽  
G.H. Erjaee
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Matrix Method ◽  
Operational Matrix ◽  
Operational Matrix Method

scholarly journals Modified operational matrix method for second-order nonlinear ordinary differential equations with quadratic and cubic terms

2020 ◽  
Vol 10 (2) ◽  
pp. 218-225
Author(s):  
Burcu Gürbüz ◽  
Mehmet Sezer
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Matrix Method ◽  
Laguerre Polynomials ◽  
Operational Matrix ◽  
Second Order ◽  
Nonlinear Ordinary Differential Equations ◽  
Algebraic Equations ◽  
Operational Matrix Method ◽  
The Matrix

In this study, by means of the matrix relations between the Laguerre polynomials, and their derivatives, a novel matrix method based on collocation points is modified and developed for solving a class of second-order nonlinear ordinary differential equations having quadratic and cubic terms, via mixed conditions. The method reduces the solution of the nonlinear equation to the solution of a matrix equation corresponding to system of nonlinear algebraic equations with the unknown Laguerre coefficients. Also, some illustrative examples along with an error analysis based on residual function are included to demonstrate the validity and applicability of the proposed method.

scholarly journals Fractional Order Operational Matrix Method for Solving Two-Dimensional Nonlinear Fractional Volterra Integro-Differential Equations

2021 ◽  
Vol 45 (4) ◽  
pp. 571-585
Author(s):  
AMIRAHMAD KHAJEHNASIRI ◽  
◽  
M. AFSHAR KERMANI ◽  
REZZA EZZATI ◽  
◽  
...  
Keyword(s):  
Integral Equation ◽  
Differential Equations ◽  
Fractional Order ◽  
Volterra Integral Equation ◽  
Matrix Method ◽  
Operational Matrix ◽  
Basis Functions ◽  
Two Dimensional ◽  
Numerical Examples ◽  
Operational Matrix Method

This article presents a numerical method for solving nonlinear two-dimensional fractional Volterra integral equation. We derive the Hat basis functions operational matrix of the fractional order integration and use it to solve the two-dimensional fractional Volterra integro-differential equations. The method is described and illustrated with numerical examples. Also, we give the error analysis.

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