APPLICATION OF ELZAKI TRANSFORM TO THE ANALYTICAL SOLUTION OF STIFF LINEAR SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS

Abstract

Stiff systems of ordinary differential equations (ODEs) are often difficult to solve because of their rapid changes and sensitivity to small variations in conditions. This study explores how the Elzaki transform can be used solve these types of equations analytically, offering an alternative to the traditional matrix method, which usually involves complex operations or exponentiation. By applying the Elzaki transform to the stiff system ODEs, we were able to find exact solutions and compare them with those from the matrix method. The outcome showed that both methods produce the same results, but the Elzaki transform approach is simpler and requires less computation. Elzaki transform proves to be a reliable and efficient method for solving stiff linear ODEs, especially in cases where traditional methods become too complicated or unstable. The Elzaki transform is a relatively new integral transform that is still not widely known, nor used.