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Método de las diferencias finitas

En análisis numérico, el método de las diferencias finitas es utilizado para calcular de manera numérica las soluciones a las ecuaciones diferenciales usando ecuaciones diferenciales finitas para aproximar derivadas.[1]

Ejemplo básico de ecuación de diferencias finitas en economía

Una ecuación sencilla en diferencias finitas

La solución se ensaya por tanteo o aproximación

Sustituyendo en la ecuación inicial

La solución será

Resolvemos

Comprobamos si la solución es correcta

Escribimos la solución general

expresa una combinación lineal de la solución

Si analizamos el Wronskiano de soluciones particulares obtendremos para t=0 y t=1

Si el Wronskiano es cero, no podemos determinar una solución correcta.
El método para resolver

es idéntico pero la solución general se escribe en función del número e.

Véase también

Bibliografía

Referencias

  1. «Metodo de las Diferencias Finitas y su ´ Aplicacion a Problemas de Electrost ´ atica». 2004. Archivado desde el original el 19 de febrero de 2018. Consultado el 6 de noviembre de 2019. 

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