Programming First Integral Method General Formula for the Solving Linear and Nonlinear Equations

Author(s)
Mohamed A. Abdoon

ABSTRACT

It’s well known that the solution of equations always uses complicated methods. In this paper the first integral method is used to find the actual solution of equations in a simple way, rather than the ex-complicated ways. Therefore, the use of first integral method makes the solution more available and easy to investigate behavior waves through its solution. First integral method is used to find exact solutions to the general formula and the applications of the results to the linear and nonlinear equations.

It’s well known that the solution of equations always uses complicated methods. In this paper the first integral method is used to find the actual solution of equations in a simple way, rather than the ex-complicated ways. Therefore, the use of first integral method makes the solution more available and easy to investigate behavior waves through its solution. First integral method is used to find exact solutions to the general formula and the applications of the results to the linear and nonlinear equations.

Cite this paper

Abdoon, M. (2015) Programming First Integral Method General Formula for the Solving Linear and Nonlinear Equations.*Applied Mathematics*, **6**, 568-575. doi: 10.4236/am.2015.63051.

Abdoon, M. (2015) Programming First Integral Method General Formula for the Solving Linear and Nonlinear Equations.

References

[1] Hirota, R. (1980) Direct Method of Finding Exact Solutions of Nonlinear Evolution Equation. In: Bullongh, R. and Caudry, P., Eds., Backlund Transformation, Springer, Berlin, 115.

[2] Wazwaz, A.M. (2004) A Sine-Cosine Method for Handling Nonlinear Wave Equations. Mathematical and Computer Modelling, 40, 499-508.

[3] Zhou, Y.B., Wang, M.L. and Wang, Y.M. (2003) Periodic Wave Solutions to a Coupled KdV Equations with Variable Coefficients. Physics Letters A, 308, 31-36.

[4] Feng, Z.S. (2002) The First Integral Method to Study the Burgers-Korteweg-de Vriesequation. Journal of Physics A, 35, 343-349.

[5] Feng, Z. (2002) On Explicit Exact Solutions for the Lienard Equation and Its Applications. Physics Letters A, 293, 50-56.

http://dx.doi.org/10.1016/S0375-9601(01)00823-4

[1] Hirota, R. (1980) Direct Method of Finding Exact Solutions of Nonlinear Evolution Equation. In: Bullongh, R. and Caudry, P., Eds., Backlund Transformation, Springer, Berlin, 115.

[2] Wazwaz, A.M. (2004) A Sine-Cosine Method for Handling Nonlinear Wave Equations. Mathematical and Computer Modelling, 40, 499-508.

[3] Zhou, Y.B., Wang, M.L. and Wang, Y.M. (2003) Periodic Wave Solutions to a Coupled KdV Equations with Variable Coefficients. Physics Letters A, 308, 31-36.

[4] Feng, Z.S. (2002) The First Integral Method to Study the Burgers-Korteweg-de Vriesequation. Journal of Physics A, 35, 343-349.

[5] Feng, Z. (2002) On Explicit Exact Solutions for the Lienard Equation and Its Applications. Physics Letters A, 293, 50-56.

http://dx.doi.org/10.1016/S0375-9601(01)00823-4