NUMERICAL SOLUTION FOR SOLVING LINEAR STIFF SYSTEMS OF FIRST-ORDER DIFFERENTIAL EQUATIONS WITH STABILITY ANALYSIS
Keywords:
stiff systems, linear differential equations, implicit Euler method, backward differentiation formulas, Runge-Kutta methods, numerical stability, computational efficiencyAbstract
This paper investigates numerical methods for solving linear stiff first-order differential equations. This is common in chemical kinetics, electrical circuit analysis, and control systems. Stiff systems have large timeframe variations. This characteristic causes steep slopes or oscillations in solutions, making numerical integration harder. Although successful,typical explicit techniques require prohibitively tiny time increments for stiff issues to prevent instability. This makes these approaches unsuitable for practical use. Due to this, implicit techniques have been developed to address these challenges.
References
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