The objective of this study is to develop a numerical approach for solving initial value problems to second-order nonlinear differential equations, employing the Piecewise Constant Argument Method (PCAM). To this end, a differential equations with piecewise constant arguments (DEPCA) is constructed, parameterized by a positive integer $n$, representing the number of subintervals. The explicit form of the unique solution to the initial value problem for the second-order DEPCA is established. Furthermore, it is proven that this solution approximates the solution to the stated problem as $n$ becomes large. Several problems derived from physical models with prescribed initial conditions are solved to validate the method. The results confirm the efficiency and high accuracy of the proposed PCAM approach.
Muminov, M. and shermukhammedov, B. (2026). A piecewise constant argument method for solving second order nonlinear differential equations. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2026.68567.3325
MLA
Muminov, M. , and shermukhammedov, B. . "A piecewise constant argument method for solving second order nonlinear differential equations", Computational Methods for Differential Equations, , , 2026, -. doi: 10.22034/cmde.2026.68567.3325
HARVARD
Muminov, M., shermukhammedov, B. (2026). 'A piecewise constant argument method for solving second order nonlinear differential equations', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2026.68567.3325
CHICAGO
M. Muminov and B. shermukhammedov, "A piecewise constant argument method for solving second order nonlinear differential equations," Computational Methods for Differential Equations, (2026): -, doi: 10.22034/cmde.2026.68567.3325
VANCOUVER
Muminov, M., shermukhammedov, B. A piecewise constant argument method for solving second order nonlinear differential equations. Computational Methods for Differential Equations, 2026; (): -. doi: 10.22034/cmde.2026.68567.3325
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