Fundamental Solution - Example

Example

Consider the following differential equation Lf = sin(x) with

.

The fundamental solutions can be obtained by solving LF = δ(x), explicitly,

.

Since for the Heaviside function H we have

.

there is a solution

Here C is an arbitrary constant introduced by the integration. For convenience, set C = − 1/2.

After integrating and taking the new integration constant as zero, we get

Read more about this topic:  Fundamental Solution

Famous quotes containing the word example:

    “Our intellect is not the most subtle, the most powerful, the most appropriate, instrument for revealing the truth. It is life that, little by little, example by example, permits us to see that what is most important to our heart, or to our mind, is learned not by reasoning but through other agencies. Then it is that the intellect, observing their superiority, abdicates its control to them upon reasoned grounds and agrees to become their collaborator and lackey.”
    —Marcel Proust (1871–1922)