00810nam a22001697a 4500040003700000082001300037100002400050245009600074260003500170300003800205500014800243500004100391500004200432502005900474546001200533650009500545  cRiphah International University   a510bMAL  aMaliha Riaz (35684)  aModified runge-kutta method based on contraharmonic mean for solving initial value problems  aIslamabadb(Unpublished)c2023  avii, 72 p.b: ill.c; 30 cm.e+CD  aSubmitted in partial fulfillment of the requirements for the degree of Master of Philosophy in Mathematics to the Department of Basic Sciences.  aIncludes bibliographical references.  aThesis supervisor: Dr. Mudassir Shams  aThesis (M.Phil)--Riphah International University, 2023  aEnglish  aMathematics vNumerical stability vZero stability vPreliminaries vSeir modelvDBSvFEAS