OICC Press International Journal of Mathematical Modelling & Computations 2228-6233 5 1 2015 03 21 NON-POLYNOMIAL SPLINE FOR THE NUMERICAL SOLUTION OF PROBLEMS IN CALCULUS OF VARIATIONS 1 14 EN Reza Jalilian Department of Mathematics, Razi University Tagh Bostan, Kermanshah Iran, Islamic Republic of Department of Mathematics J. Rashidinia K. Farjian H. Jalilian Journal Article 2015 03 21 A Class of new methods based on a septic non-polynomial spline function for the numerical solution of problems in calculus of variations is presented. The local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th, are obtained. The inverse of some band matrixes are obtained which are required in proving the convergence analysis of the presented method. Convergence analysis of these methods is discussed. Numerical results are given to illustrate the eciency of methods and compared with the methods in [28-32].