A Conventional Approach for the Solution of the Fifth Order Boundary Value Problems Using Sixth Degree Spline Functions

Affiliation(s)

Kakatiya Institute of Technology and Sciences, Warangal, India.

Varadha Reddy College of Engineering, Warangal, India.

Kakatiya Institute of Technology and Sciences, Warangal, India.

Varadha Reddy College of Engineering, Warangal, India.

ABSTRACT

In this communication we have used Bickley’s method for the construction of a sixth order spline function and apply it to solve the linear fifth order differential equations of the form y^{x}(x)+g (x)y(x)= r(x) where g(x) and r(x) are given functions with the two different problems of different boundary conditions. The method is illustrated by applying it to solve some problems to demonstrate the application of the methods discussed.

Cite this paper

P. Kalyani, P. Rao and A. Rao, "A Conventional Approach for the Solution of the Fifth Order Boundary Value Problems Using Sixth Degree Spline Functions,"*Applied Mathematics*, Vol. 4 No. 4, 2013, pp. 583-588. doi: 10.4236/am.2013.44082.

P. Kalyani, P. Rao and A. Rao, "A Conventional Approach for the Solution of the Fifth Order Boundary Value Problems Using Sixth Degree Spline Functions,"

References

[1] W. G. Bickley, “Piecewise Cubic Interpolation and Two Point Boundary Value Problems,” Computer Journal, Vol. 11, No. 2, 1968, pp. 206-208. doi:10.1093/comjnl/11.2.206

[2] E. A. Boquez and J. D. A. Walker, “Fourth Order Finite Difference Methods for Two Point Boundary Value Problems,” IMA Journal of Numerical Analysis, Vol. 4, No. 1, 1984. pp. 69-82. doi:10.1093/imanum/4.1.69

[3] M. M. A. Chawla, “Fourth Order Tridiagonal Finite Difference Method for General Two Point Boundary Value Problems with Mixed Boundary Conditions,” Journal of the Institute of Mathematics and Its Applications, Vol. 21, No. 1, 1978, pp. 83-93. doi:10.1093/imamat/21.1.83

[4] P. S. Rama Chandra Rao, “Solution of Fourth Order Boundary Value Problems Using Spline Functions,” Indian Journal of Mathematics and Mathematical Sciences, Vol. 2, No. 1, 2006, pp. 47-56.

[5] P. S. Rama Chandra Rao, “Special Multistep Methods Based on Numerical Differentiation for Solving the Initial Value Problem,” Applied Mathematics and Computation, Vol. 181, No. 1, 2006, pp. 500-510. doi:10.1016/j.amc.2005.12.063

[6] P. S. Rama Chandra Rao, “Solution of a Class of Bondary Value Problems Using Numerical Integration,” Indian Journal of Mathematics and Mathematical Sciences, Vol. 2, No. 2, 2006, pp. 137-146.

[7] P. S. Rama Chandra Rao, “Solution of Initial Value Problems by Spectial Multistep Methods,” Indian Journal Mathematics and Mathematical Sciences, Vol. 2. No. 2, 2006, pp. 201-208.

[1] W. G. Bickley, “Piecewise Cubic Interpolation and Two Point Boundary Value Problems,” Computer Journal, Vol. 11, No. 2, 1968, pp. 206-208. doi:10.1093/comjnl/11.2.206

[2] E. A. Boquez and J. D. A. Walker, “Fourth Order Finite Difference Methods for Two Point Boundary Value Problems,” IMA Journal of Numerical Analysis, Vol. 4, No. 1, 1984. pp. 69-82. doi:10.1093/imanum/4.1.69

[3] M. M. A. Chawla, “Fourth Order Tridiagonal Finite Difference Method for General Two Point Boundary Value Problems with Mixed Boundary Conditions,” Journal of the Institute of Mathematics and Its Applications, Vol. 21, No. 1, 1978, pp. 83-93. doi:10.1093/imamat/21.1.83

[4] P. S. Rama Chandra Rao, “Solution of Fourth Order Boundary Value Problems Using Spline Functions,” Indian Journal of Mathematics and Mathematical Sciences, Vol. 2, No. 1, 2006, pp. 47-56.

[5] P. S. Rama Chandra Rao, “Special Multistep Methods Based on Numerical Differentiation for Solving the Initial Value Problem,” Applied Mathematics and Computation, Vol. 181, No. 1, 2006, pp. 500-510. doi:10.1016/j.amc.2005.12.063

[6] P. S. Rama Chandra Rao, “Solution of a Class of Bondary Value Problems Using Numerical Integration,” Indian Journal of Mathematics and Mathematical Sciences, Vol. 2, No. 2, 2006, pp. 137-146.

[7] P. S. Rama Chandra Rao, “Solution of Initial Value Problems by Spectial Multistep Methods,” Indian Journal Mathematics and Mathematical Sciences, Vol. 2. No. 2, 2006, pp. 201-208.