How to solve system of second order ordinary differential equations numerically? Global finite element system

I have system of equations, and how it can be solved in general form or at least in this form which is given in below? This is the global finite element system with two linear shape functions.

Answer 1

[Kiran Felix Robert]

Hi Rakhymzhan,

You can refer to the following documents for solving second order numerical equations numerically and symbolically,

1. Solve a second order Differential Equation Numerically
2. Solve Differential Equations

Kiran Felix Robert

[Rakhymzhan Kazbek]

I mean, how to solve in this partcular case when element of matrices are nonlinear and how it can be implemented? I knew all these standards links from matlab.