Approximate solutions to a parameterized sixth order boundary value problem

Approximate solutions to a parameterized sixth order boundary value problem

In this paper, the homotopy analysis method (HAM) is applied to solve a parameterized sixth order boundary value problem which, for large parameter values, cannot be solved by other analytical methods for finding approximate series solutions. Convergent series solutions are obtained, no matter how large the value of the parameter is.

Positive Solutions to a Singular Second Order Boundary Value Problem

In this paper, we establish some criteria for the existence of positive solutions for certain two point boundary value problems for the singular nonlinear second order equation −(ru ) + qu = λf (t, u ) on a time scale T. As a special case when T = R, our results include those of Erbe and Mathsen [11]. Our results are new in a general time scale setting and can be applied to difference and q-dif...

Multiple Positive Solutions to a Fourth-order Boundary-value Problem

We study the existence, localization and multiplicity of positive solutions for a nonlinear fourth-order two-point boundary value problem. The approach is based on critical point theorems in conical shells, Krasnosel’skĭı’s compression-expansion theorem, and unilateral Harnack type inequalities.

Positive Solutions to a Second-Order Discrete Boundary Value Problem

Numerical solution for boundary value problem of fractional order with approximate Integral and derivative

Approximating the solution of differential equations of fractional order is necessary because fractional differential equations have extensively been used in physics, chemistry as well as engineering fields. In this paper with central difference approximation and Newton Cots integration formula, we have found approximate solution for a class of boundary value problems of fractional order. Three...