Approximate solution of complex differential equations for a rectangular domain with Taylor collocation method

In this study, Taylor collocation method is investigated for the approximate computation of high-order linear complex differential equations. Using the collocation points on any rectangular domain in the complex plane, the method transforms the given complex differential equation and the mixed conditions to matrix equation with unknown Taylor coefficients. By means of the obtained matrix equations, the Taylor coefficients can be easily computed. Hence, the finite Taylor series approach is obtained. Also, examples are presented and the results are discussed.

[1]  M. Hadizadeh,et al.  A Taylor polynomial approach for solving high-order linear Fredholm integro-differential equations in the most general form , 2007, Int. J. Comput. Math..

[2]  Yik-Man Chiang,et al.  Oscillation Results of Certain Higher Order Linear Differential Equations with Periodic Coefficients in the Complex Plane , 1997 .

[3]  R. Kanwal,et al.  A Taylor expansion approach for solving integral equations , 1989 .

[5]  Mehmet Sezer,et al.  A Taylor Collocation Method for the Solution of Linear Integro-Differential Equations , 2002, Int. J. Comput. Math..

[6]  Risto Korhonen,et al.  GROWTH ESTIMATES FOR SOLUTIONS OF LINEAR COMPLEX DIFFERENTIAL EQUATIONS , 2004 .

[7]  Mehmet Sezer,et al.  A method for the approximate solution of the second‐order linear differential equations in terms of Taylor polynomials , 1996 .

[8]  Mehmet Sezer,et al.  A chebyshev collocation method for the solution of linear integro-differential equations , 1999, Int. J. Comput. Math..

[9]  Mehmet Sezer,et al.  A new polynomial approach for solving difference and Fredholm integro-difference equations with mixed argument , 2005, Appl. Math. Comput..

[10]  Murray R. Spiegel,et al.  Theory and Problems of Complex Variables , 1974 .

[11]  Mehmet Sezer,et al.  Chebyshev polynomial solutions of systems of high-order linear differential equations with variable coefficients , 2003, Appl. Math. Comput..

[12]  L. Ahlfors.  Complex Analysis , 1979 .

[13]  M. Sezer,et al.  A TAYLOR POLYNOMIAL APPROACH FOR SOLVING HIGH-ORDER LINEAR FREDHOLM INTEGRODIFFERENTIAL EQUATIONS , 2000 .

[14]  Mehmet Sezer,et al.  Taylor polynomial solutions of systems of linear differential equations with variable coefficients , 2005, Int. J. Comput. Math..

[15]  Mehmet Sezer,et al.  The approximate solution of high-order linear Volterra-Fredholm integro-differential equations in terms of Taylor polynomials , 2000, Appl. Math. Comput..

[16]  Mehmet Sezer,et al.  The approximate solution of high-order linear difference equations with variable coefficients in terms of Taylor polynomials , 2005, Appl. Math. Comput..