TY - JOUR
AU - Okor, Tega
AU - Nwachukwu, Grace, Chinyere
PY - 2022/10/05
Y2 - 2022/12/03
TI - Generalized Cash-type Second Derivative Extended Backward Differentiation Formulas for Stiff systems of ODEs: Extended backward differentiation
JF - Journal of the Nigerian Mathematical Society
JA - JNMS
VL - 41
IS - 2
SE - Articles
DO -
UR - https://ojs.ictp.it/jnms/index.php/jnms/article/view/810
SP - 163 - 191
AB - <pre>In this paper, a generalized Cash-type second derivative extended backward differentiation formulas (GCE2BD) <br>is developed as boundary value methods (BVMs) for the numerical solution of stiff systems of ordinary differential<br>equations (ODEs). The proposed class of methods is O<sub>v,(k+1)-v</sub>-stable and A<sub>v,(k+1)-v</sub>-stable with (v,(k+1)-v)-boundary <br>conditions and order k+3 for all values of the step-length k >= 1.The class of methods proposed is exceptional for <br>the numerical solution of stiff systems whose Jacobians have some relatively large eigenvalues near the imaginary <br>axis. The accuracy and efficiency of the constructed methods are examined in some details via the numerical <br>experiments carried out on some well-known linear and non-linear stiff systems using the boundary value techniques<br>such that the numerical solution of a problem is obtained simultaneously on the entire interval of integration.<br>The new class of methods is found to compare favorably with existing standard methods in the literature.</pre>
ER -