NUMERICAL SOLUTIONS OF HERMITE DIFFERENTIAL EQUATIONS USING LEGENDRE MULTIWAVELETS - Meenu Devi; Sunil Rawan; Sushil Chandra Rawan; Vineet Kishore Srivastava (PATTIMURA UNIVERSITY, 2026)
This paper presents a numerical method for solving Hermite differential equations (HDEs) using operational integration matrices derived from Legendre multiwavelets of linear, quadratic, and cubic orders. The proposed technique transforms HDEs into algebraic systems, enabling efficient and accurate numerical solutions. Through several illustrative examples, the method’s effectiveness is demonstrated, with Cubic Legendre Multiwavelets (CLMW) exhibiting superior accuracy in approximating exact solutions.