The Homotopy Perturbation Method to Solve Initial Value Problems of First Order with Discontinuities
نویسندگان
چکیده
In this work, the homotopy perturbation method (HPM) is used to solve initial valueproblems of first order with various types discontinuities. The numerical results obtained (arecompared) using traditional HPM, and integral equation nth thesolution Simpson Trapezoidal Rules demonstrate that are extremely accurate when compared exact solution. maximumabsolute error, ‖ . , maximum relative residual expectedconvergence also provided.
منابع مشابه
The comparison of optimal homotopy asymptotic method and homotopy perturbation method to solve Fisher equation
In recent years, numerous approaches have been applied for finding the solutions of functional equations. One of them is the optimal homotopy asymptotic method. In current paper, this method has been applied for obtaining the approximate solution of Fisher equation. The reliability of the method will be shown by solving some examples of various kinds and comparing the obtained outcomes with the ...
متن کاملHomotopy perturbation method for solving sixth-order boundary value problems
In this paper, we apply the homotopy perturbation method for solving the sixth-order boundary value problems by reformulating them as an equivalent system of integral equations. This equivalent formulation is obtained by using a suitable transformation. The analytical results of the integral equations have been obtained in terms of convergent series with easily computable components. Several ex...
متن کاملSolving the non linear system of third order boundary value problems by using He's homotopy perturbation method
متن کامل
First Order Initial Value Problems
where the initial time, t0, is a given real number, the initial position, ~ ξ0 ∈ IR, is a given vector and ~ F : IR × IR → IR is a given function. We shall assume throughout these notes that ~ F is C. By definition, a solution to the initial value problem (1) on the interval I (which may be open, closed or half–open, but which, of course, contains t0) is a differentiable function ~x(t) which obeys
متن کاملFirst Order Initial Value Problems
where the initial time, t0, is a given real number, the initial position, ~ ξ0 ∈ IR, is a given vector and ~ F : IR × IR → IR is a given function. We shall assume throughout these notes that ~ F is C. By definition, a solution to the initial value problem (1) on the interval I (which may be open, closed or half–open, but which, of course, contains t0) is a differentiable function ~x(t) which obeys
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Ma?alla? al-r?fidayn li-?ul?m al-??sib?t wa-al-riy??iyy??
سال: 2022
ISSN: ['1815-4816', '2311-7990']
DOI: https://doi.org/10.33899/csmj.2022.176592